The numerical value of the vertical velocity of the car at time t=0 is 4.91 meters per second.
Given,
t = 0.25 s
y = 0.75 m
α = 0.95 rad/s²
ω = 6.3 rad/s
Wf=6.54 rad/sec
V=wr
6.54*0.75
V=4.91 m/s
The classic example of independent motions along different axes is projectile motion. Projectile motion is the combination of two separate linear motions. The horizontal motion doesn’t affect the vertical motion, and vice versa. Since there is no acceleration in the horizontal direction (ignoring air resistance), the projectile moves with constant velocity in the x direction.
If an object slides down a friction less plane inclined at angle θ, the acceleration down the plane is g sin θ, because the component of g (the downward acceleration due to gravity) that points along the plane is g sin θ. (There is no acceleration perpendicular to the plane because the normal force from the plane cancels the component of the gravitational force perpendicular to the plane.
Another type of 2-D motion is circular motion. If an object is moving in a circle of radius r with speed v at a given instant, then the (inward) radial component of the acceleration vector a equals. This radially inward acceleration is called the centripetal acceleration. If additionally the object is speeding up or slowing down as it moves around the circle.
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If A and B are two Hermitian operators, showthat AB and BA may
not be Hermitian, but that (AB + BA) andi(AB-BA) are both
hermitian. Prove that the expectation value ofA2 is
always real and non-negative. If A2=2,find the
eigenvalues of A
A and B being Hermitian operators means that they are equal to their own conjugate transpose.
What is a Hermitian operator?
A Hermitian operator is an operator that is equal to its own complex conjugate. This means that if an operator A is Hermitian, then A=A*. This property is important in quantum mechanics, since it guarantees that the eigenvalues of the operator are real.
AB ≠ BA
(AB + BA) = (A + B)*(A + B) = A*A + A*B + B*A + B*B
(AB + BA) is Hermitian since the conjugate transpose of a sum is the sum of the conjugate transposes.
i(AB-BA) = i(A - B)*(A - B) = -iA*A + iA*B -iB*A + iB*B
i(AB-BA) is Hermitian since the conjugate transpose of a sum is the sum of the conjugate transposes.
The expectation value of A2 is always real and non-negative since A2 is Hermitian and thus equal to its own conjugate transpose, which implies its eigenvalues are real.
If A2 = 2, then A can have eigenvalues of ±√2.
Hence, eigenvalues of A is ±√2.
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Help!!!!!
Question answer in the photo
Answer: D
Explanation:
The wind will begin to blow the sediments of the arch away, causing the arched structure to become thinner over time. Therefore, the best answer is option D.
What velocity must a 2. 25 kg croquet mallet have in order to have the same momentum as 1. 25 kg ball that has a momentum 6. 25 kg•m/s to the west
2.78 m/s to the west velocity must a 2. 25 kg croquet mallet have in order to have the same momentum as 1. 25 kg ball that has a momentum 6. 25 kg•m/s to the west.
Given,
Mass = 2.25kg
Momentum = 6.25 kg•m/s
To find,
Velocity
Formula used,
Momentum = Mass x velocity
Calculation,
6.25 kg•m/s = 2.25 kg x velocity
Velocity = 6.25/2.25
Velocity = 2.78 m/s
The conservation of momentum principle asserts that the quantity of momentum inside a problem domain remains constant; momentum is not generated nor destroyed, but only modified by the action of forces as defined by Newton's equations of motion.
Newton's third law says that for every force exerted by object A on object B, object B exerts an equal but opposite force in magnitude and direction. Newton utilised this concept to create the law of conservation of momentum.
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Copper (Cu) reacts with phosphorus (P) to produce copper (II) phosphide.
so far all ive got is Cu₂ +4P --> _____
Answer: The answer is Cu+ P4 = Cu3P2
Which after balancing would be, 6Cu + P4 = 2Cu3p2
Explanation: Copper (Cu) is a metal and Phosphorous (P) is a non-metal. Metals and Non-metals combine to form ionic compounds where there is a transfer of ions from metal to non-metal.
Phosphorous has 5 valence electrons in its outer shell and Copper has 2 valence electrons. Following the octet rule, which means that the outer shell should have 8 electrons to be complete we see that combining these two metals on combining have electrons insufficient so we combine till we reach the octet structure. In this case, it happens when there are three copper and two phosphorous. We see that there are no more valence electrons. So it forms Copper II Phosphide, where the two indicates the charge of Copper.
Then we move on to balance both the sides of the equation, upon placing one number after the other to make the numerical value of elements equivalent to the other. Which gives us the answer.
a total of 10.0j of work is done in accelerating a 20-n object from rest across a horizontal frictionless table. what is the total kinetic energy gained by the object
The total kinetic energy gained by the object when accelerating a 20-n object from rest across a horizontal frictionless table is 10.0 J.
How do you determine the total kinetic energy?To determine the total kinetic energy gained by the object, we can use the work-energy principle, which states that the work done on an object is equal to the change in kinetic energy of the object.
Work done = change in kinetic energy
W = Kf - Ki
where
W = work done (10.0 J)
Kf = final kinetic energy
Ki = initial kinetic energy (0 J, since the object is at rest)
Given the information provided, we know that a total of 10.0 J of work is done in accelerating the 20-n object from rest.
So,
Kf = W + Ki
Kf = 10.0 J + 0 J
Kf = 10.0 J
Therefore, the total kinetic energy gained by the object is 10.0 J
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a tennis player hits a tennis ball with a force of 15N and moves it 25m . of the tennis players power output was 750W, find out how long they did work on the tennis ball for
When we do, we make sure to measure our mass in kilograms. We determine that F is equal to 124.26 newtons by entering these numbers into our calculator.
That is the average magnitude of the force applied to the tennis ball.
How is the force of a tennis serve calculated?The equation that Newton was referring to is shown by a serve. You can calculate the total force that was applied by the tennis racket to the ball by multiplying the weight of the racket by the speed at which the player swings their racquet.
After serving, how much does a tennis ball slow down?An average 120-mph serve slows to 82 mph before the bounce, 65 mph after the bounce, and 55 mph at the opponent's racket, according to tennis instructor and analyst John Yandell.
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A 1.41-kg block slides across a rough surface such that it slows down with an acceleration of 1.10 m/s2. What is the coefficient of kinetic friction between the block and the surface
The coefficient of kinetic friction between the block and the surface is 0.11.
The coefficient of kinetic friction can be found using the equation:
friction = force of friction = coefficient of kinetic friction * normal force
The normal force is equal to the weight of the object, which can be calculated as weight = mass * acceleration due to gravity
The force of friction can be calculated using the equation:
friction = force of friction = coefficient of kinetic friction * weight
The coefficient of kinetic friction can be found by rearranging the equation and substituting the known values:
coefficient of kinetic friction = friction / weight
= (1.10 m/s2) / (1.41 kg * 9.8 m/s2)
= 0.11
So, the coefficient of kinetic friction between the block and the surface is 0.11.
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Just as a light-year is the distance that light can travel in 1 year, we define a light-second as the distance that light can travel in 1 second, a light-minute as the distance that light can travel in 1 minute, and so on. Calculate the distance in both kilometers and miles represented by each of the following:
Approximately 5.878 x 1012 miles or 9.461 x 1015 meters, a light-year is the maximum distance light can travel in a single year..
What is light year and calculate the distance in both kilometers and miles?A light year is the distance light travels in one year, approximately 9.461 x 10^15 meters or 5.878 x 10^12 miles.A light-second is the distance that light can travel in one second, which is approximately 299,792,458 meters or approximately 186,282.397 miles.A light-minute is the distance that light can travel in one minute, which is approximately 17,987,000,000 meters or approximately 11,162,913.12 miles.A light-hour is the distance that light can travel in one hour, which is approximately 1,079,000,000,000 meters or approximately 669,573,787.2 miles.A light-day is the distance that light can travel in one day, which is approximately 25,902,000,000,000 meters or approximately 16,093,441,632 miles.A light-year is the distance that light can travel in one year, which is approximately 9.461 x 10^15 meters or approximately 5.878 x 10^12 miles.To learn more about light year refer:
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A cylindrical bucket of liquid (density rho) is rotated about its symmetry axis, which is vertical. If the angular velocity is ω, show that the pressure at a distance r from the rotation axis is P=P 0+ 21rhoω 2r 2where P 0 is the pressure at r=0,
Answer:
To derive the formula for the pressure at a distance r from the rotation axis, you can use the principle of hydrostatic equilibrium. This states that the pressure at a point in a fluid is equal in all directions and the net force on a fluid element is equal to zero.
Consider a small cylindrical element of fluid at a distance r from the rotation axis, as shown in the diagram below. The dimensions of the element are dr in the radial direction, 2πr in the circumferential direction, and h in the vertical direction. The weight of the element is equal to the product of its volume, density, and the acceleration due to gravity: W = (2πr)(dr)(h)(ρ)(g). The pressure at the top and bottom faces of the element is P + dP, where P is the pressure at the point and dP is a small change in pressure. The forces acting on the element are the weight of the element, the pressure force at the top face, and the pressure force at the bottom face.
[asy]
unitsize(2cm);
pair P1, P2, P3, P4;
P1 = (0,0);
P2 = (1,0);
P3 = (1,1);
P4 = (0,1);
draw((-0.5,0)--(1.5,0));
draw((0,-0.5)--(0,1.5));
draw(P1--P2--P3--P4--cycle);
draw((0.5,0)--(0.5,1));
draw((0.25,0)--(0.25,1));
draw((0.75,0)--(0.75,1));
label("$r$", (0.5,1.5), red);
label("$
10) An ice cube of mass 0.046 kg and temperature -14 C is heated until it is now fully melted and at a temperature of 11C now. What percentage of the total energy was used to melt the ice
90.23 % percentage of the total energy was used to melt the ice.
Define Energy?Energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed.
Calculation -:Total energy used from -[tex]14^{o}[/tex]C to [tex]11^{o}[/tex]C
= [tex]m_{i}c_{i} T_{i}[/tex] + [tex]m_{i} L_{f}[/tex] +[tex]m_{w} c_{w}[/tex]Δ[tex]T_{2}[/tex]
= (0.013×2200×8) + (0.031×334000) + (0.013×486×11)
= 400.4 + 4342 + 69.498
= 4811.898 J
% energy used to melt = 4342/4811.898 × 100
= 90.23 %
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when the time of day for a certain ship is 12 noon the time of day at the Prime Meridian is 5 p.m. what's the ship's longitude
The required longitude of the certain ship when the time of the day is 12 noon at the Prime Meridian is 5 p.m is 75° West.
The sun is highest in London, but will not pass the ship for another 5 hours.
Given that,
The time of day for a certain ship is 12 noon at the Prime Meridian is 5 p.m.
The ship must be five hours west of Greenwich since the sun goes from east to west.
Each hour of sun motion is 15° of longitude. The ship is located at (5 x 15°) = 75° West longitude.
Thus, the ship's longitude is 75° West.
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Written problem: I find that I can blow 1000 cm3 of air through a drinking straw in 1.3 s. The diameter of the straw is 5 mm. Find the velocity of the air through the straw.
Answer:
Below
Explanation:
Diameter of straw = .5 cm then the radius = .25 cm
AREA of the straw = pi r^2 = pi ( .25 cm)^2 = .19635 cm^2
Now we need to find the LENGTH necessary to have a volume of 1000 cm^3
1000 cm^3 = L * . 19635 cm^2
L = 5.092.958 cm <=== your blowing covers this distance in 1.3 s
5092.958 cm / 1.3 s = 3917.7 cm / s = 39.2 m/s
Due to the drivers not paying attention, a small car and a big truck collide, both are initially moving at 25 mph towards each other. Compare the magnitude of the force the truck exerts on the car to the magnitude of the force the car exerts on the truck. Which force is greater? Which vehicle would you rather ride in? Describe why you made your choice.
As a result, the amount of force the truck exerts on the automobile is equal to the amount of force the truck exerts on the car.
As per Newton's third law of motion
If object A applies a force to object B, then object B must apply a force to object A in the opposite direction and of equal strength. This rule illustrates a symmetry in nature whereby forces always occur in pairs and that no body can exert a force without also being subjected to one.
Because the accident is a head-on collision, according to Newton's third law, both the automobile and the truck will exert equal force against one another.
As a result, it will be safe to ride in the truck since the automobile will accelerate more quickly under the same force due to its lighter weight. Bigger acceleration results in a greater change in velocity, which increases the driver's workload.
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A 10.0-g bullet is fired into a stationary block of wood having mass m 5 5.00 kg. The bullet imbeds into the block. The speed of the bullet-plus-wood combination immediately after the collision is 0.600 m/s. What was the original speed of the bullet
The original speed of the bullet was 300.6 m/s.
What is the best meaning of mass?A measure of the amount of matter contained in or constituting a physical body. In classical mechanics, the mass of an object is related to the force required to accelerate it and hence is related to its inertia, and is essential to Newton's laws of motion.
Given:
mV bi +MV wi =mV b +M Vwf
where m= mass of bullet =10 g=10^−2 ∣kg
M= mass of wood block =5 kg
V bI = initial mass of bullet
Vwi = initial mass of wood block and V bf =V wf
=0.06 m/s 10 −2 Vbi+0(10 −2 +5)0.6 V
bi = 10 −2 5.01×0.6 V
bi =300.6 m/s
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5. Is the motion of the stars around Polaris (NCP) due to the __________rotation (daily motion) or ___________revolution (yearly motion) of Earth
The motion of the stars around Polaris (NCP) is due to rotation (daily motion) of Earth.
Polaris is a star in Ursa Minor's northern circumpolar constellation. It is known as Ursae Minoris and is also known as the North Star or Pole Star. With an apparent brightness of roughly 1.98, it is the brightest star in the constellation and may be seen with the bare eyes at night. The star's location is less than one degree from the north celestial pole, making it the current northern pole star. The star's constant location in the Northern Sky makes it ideal for navigation.
Its distance is considered as part of the cosmic distance ladder since it is the nearest Cepheid variable. The updated Hipparcos stellar parallax distance to Polaris is approximately 433 light-years (133 parsecs), whereas the successor mission Gaia distance is around 448 light-years (137 parsecs). Other techniques of calculation produce significantly disparate results.
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From the viewpoint of an alien astronomer, how does Jupiter affect observations of our Sun?
a) It causes the Sun to move in a small ellipse with an orbital period of about 12 years.
b) It makes the Sun periodically get somewhat brighter.
c) It makes the Sun appear dimmer when viewed with infrared light.
d) It causes the Sun to move in a small ellipse in the sky, with the same ellipse repeated every night.
Jupiter affect observations of the Sun, from the viewpoint of an alien astronomer, by causing the Sun to move in a small ellipse with an orbital period of about twelve years. The correct option is option a.
Being the fifth closer planet to our Sun, Jupiter is the biggest planet in our Solar System. Jupiter is one of the gas giants in the Solar System.
From the Sun, Jupiter's average distance is about 480 million miles, and it takes nearly twelve years for Jupiter to make one revolution. Jupiter has a ring, albeit flat and small, like the rest of the gas giants. Jupiter's rotation is the fastest of all planets in the Solar System, rotating once on its axis every ten hours.
From the viewpoint of an alien astronomer outside our Solar System, the Sun will look as if it orbits Jupiter and takes 12 years to complete a revolution. Planets in general have orbits that are elliptical.
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Which type of engine takes in air, accelerates it, and pushes it out the exhaust nozzle to produce thrust that pushes the aircraft forward
A jets engine is a device that produces a strong pushing force known as thrust out of liquid fuel that is high in energy.
What do aircraft turbine engines do?A rotary engine called a gas turbine converts the flow of combustion into energy.Axial or centrifugal compressors (or both) can be used to boost air pressure and temperature before it enters the combustion chamber. Ambient air is pulled into the engine intake.
How is thrust produced by a jet engine?By raising internal engine pressure, jet or rocket engines generate thrust.This higher pressure inside the jet and rocket engine causes the forward force to be greater than the backward force.
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Four particles with masses 4 kg, 4 kg, 4 kg, and 7 kg are connected by rigid rods of negligible mass as shown. Assume the system rotates in the xy plane about the z axis (origin, O) with an angular speed of 9 rad/s. Find the rotational energy of the system about the x axis.
The rotational Kinetic energy of the system about X axis is 24624 J.
Let the distance of the mass 4kg, from O is r1,
r = √(4² + 4²)
r = √32m
The distances of masses to the rotation axis is same -
say,
r1 = r2 = r3 =r4 = √32
Hence,
I = ∑ mi r1²
I = r² ∑(m1 + m + m3 + m4)
= 32(19)
I = 608 Kg m²
We know that rotational energy of system is given as,
K = 1/2 Iw²
Given,
W = 9 rad/sec
∴ K = 1/2 × 608 × 9²
K = 24624 J
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A mass of 0.343 kg moves down a 5 meter ramp in 5.8 seconds. What is its velocity and kinetic energy
According to the given information the velocity is .0148 m/s2 and the kinetic energy is 3.78 J.
What is the straightforward meaning of velocity?The movement that an item or particle experiences with regard to time is expressed vectorially as velocity. One metre per second (m/s) is the accepted unit of flow speed (also known as speed).
What does velocity in SI mean?The metric speed unit is the meter per minute (m/s). A different way to express velocity magnitude is in centimeters per second (cm/s).
vilocity = 5/(5.8×5.8)
= 0.148
kinetic energy = 1/2mv^2
= 1/2 × (0343 × 0.148×0.148)
= 3.78 J
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If a circle has a circumference of 25.1 cm compare where the object would have been if it had gone in a straight line at 4 cm/s for 6.28 seconds(no acceleration) to where it is after it has gone around the circle for 6.28 at 4.0cm/s
The object would have returned to its initial starting point if it had travelled round a circle.
What is the distance travelled by the object?
The distance travelled by the object is determined from the product of speed of the object and the time of motion of the object.
D = vt
where;
v is the speed of the object = 4 cm/st is the time of motion of the object = 6.28 sThe distance travelled by the object is calculated as follows;
D = ( 4 cm / s ) x ( 6.28 s )
D = 25.1 cm
Thus, at the given time and speed the object would have travelled round the circle. That is the object would have made one complete revolution.
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How long does it take a plane, traveling at a constant speed of 130 m/s, to fly once around a circle whose radius is 2650 m
51.6 seconds long does it take a plane, traveling at a constant speed of 130 m/s, to fly once around a circle whose radius is 2650 m.
The time it takes for an object to travel once around a circle of radius r at a constant speed v can be found using the equation:
T = 2 x π x r ÷ v
where T is the time in seconds, pi is approximately 3.14, r is the radius of the circle in meters, and v is the speed of the object in meters per second.
Given a constant speed of 130 m/s and a radius of 2650 m, the time it would take for a plane to fly once around the circle would be:
T = 2 x π x 2650 m / 130 m/s
T = 51.6 sec
So, it would take approximately 51.6 seconds for a plane traveling at a constant speed of 130 m/s to fly once around a circle whose radius is 2650 m.
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A simple pendulum has a period of 3 seconds . If the value of ‘g’ is taken as 9.98 ms-2 calculate the length of the pendulum.
Answer: The length of the pendulum is approximately 2.495 meters.
Explanation:
The period of a simple pendulum is the time it takes for the pendulum to swing back and forth through one full oscillation. The period of a simple pendulum is related to the length of the pendulum and the acceleration due to gravity (g) by the formula:
Period = 2 * pi * sqrt(length / g)
In this case, you are given that the period of the pendulum is 3 seconds and the value of g is 9.98 ms-2. You can use these values to solve for the length of the pendulum using the formula above.
Substituting in the values given, you get:
3 = 2 * pi * sqrt(length / 9.98)
Solving for length, you get:
length = (3 / (2 * pi))^2 * 9.98
= 0.5^2 * 9.98
= 0.25 * 9.98
= 2.495
Therefore, the length of the pendulum is approximately 2.495 meters.
i need help with this can give a heart or like if its right
The new electrostatic force between the charges, given that q₁ is reduced to 1/2q₁ and q₂ is tripped is 3/2Fₑ (Option C)
How do I determine the new electrostatic force?First, we shall determine the initial electrostatic force between the charges. Details below:
First Charge (q₁) = q₁second Charge (q₂) = q₂Electric constant (K) = KDistance apart (r) = rInitial electrostatic force (F) = Fₑ =?F = Kq₁q₂ / r²
Fₑ = Kq₁q₂ / r²
Finall, we shall determine the new electrostatic force. The is illustrated below:
First Charge (q₁) = 1/2q₁second Charge (q₂) = 3q₂Electric constant (K) = KDistance apart (r) = rNew electrostatic force (F) =?F = Kq₁q₂ / r²
F = (K × 1/2q₁ × 3q₂) / r²
F = 3/2Kq₁q₂ / r²
But,
Fₑ = Kq₁q₂ / r²
Thus
F = 3/2Fₑ
Thus, we can conclude that the new electrostatic force is 3/2Fₑ (Option C)
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How do you think the speed a satellite fall towards Earth compares to the speed it is moving forward
The speed a satellite fall towards Earth compares to the speed it is moving forward If the speed drops, it will fall toward the earth.
We can say that satellite speed has a significant impact on satellite motion because if a satellite's speed is reduced by half, it will fall towards the earth because it is drawn in by the earth's gravitational pull. However, if a satellite's speed is doubled, it will travel into space because the earth's gravitational pull will no longer hold it in orbit.
When a satellite is moving quickly, the force of gravity may not be able to hold it in orbit. If it moves slowly, it won't make enough progress to resist gravity's pull and collide with the object it is orbiting.
Rockets are used to put the majority of satellites into orbit. When the pull of Earth's gravity and the satellite's speed are equal, the satellite circled the planet. Without this equilibrium, the satellite would either fall back to Earth or shoot off into space in a straight path.
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A boy exerts a force of 225 N on a lever (Links to an external site.) to raise a 1250 N rock a distance (Links to an external site.) of 0.13 m. If the lever is frictionless, how far did the boy have to move his end of the lever
If the lever is frictionless, to raise the rock a distance of 0.13 m, then the boy has to move the lever to 0.72 m.
An external force that acts upon an object results in a motion of the object, then it is called a work done upon the object by that force.
Given that the external force on a lever is 225 N and on a rock is 1250 N. The distance of motion by the rock is 0.13 m.
Hence the work done by the lever will be equivalent to the work done by the rock to move a particular distance.
Work (Lever) = Work (Rock)
F(lever) x D (lever) = F (rock) x D (rock)
225x D(lever)= 1250 x0.13
D(lever) is 0.72 m
Hence we can conclude that the distance of the motion by the lever is 0.72 m.
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A truck travels due east for a distance of 1.4 km, turns around and goes due west for 7.7 km, and finally turns around again and travels 2.6 km due east. (a) What is the total distance that the truck travels
The total distance that the truck travels is 11.7 km
Part (a)
The algebraic sum of the various distances results in the total distance covered by the trucks.
DT = d1 + d2 + d3
So, total distance that the truck travels = 1.4 + 7.7 + 2.6 = 11.7 km
Part (b) Question is missing :
(b) What are the magnitude (in km) and direction of the truck's displacement? (Enter a number.)
magnitude #? km
direction? east, west or neither.
The quickest route taken by the object to get from one spot to another is called displacement.
As the truck travels in three directions, from east to west to east, it begins out from the east. Think of the east as being good and the west as being negative. As a result, the displacement can be calculated as shown below.
D =d1 - d2 + d3 = 1.4 - 7.7 + 2.6 = 1.4 - 5.1 = -3.7 km
Here, the negative sign shows that the truck has displaced in the west direction.
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Because of the Doppler effect, a light- or sound-emitting object moving toward you has a ________ compared to a stationary object.
Because of the Doppler effect, a light- or sound-emitting object moving toward you has a lower amplitude compared to a stationary object.
The Doppler effect is generally defined as the shift in wave frequency (whether it be sound or light) caused by relative motion between the wave source and the observer. Every time a source wave moves in reference to the observer, this effect can be seen.
The Doppler effect allows astronomers to determine the frequency of light waves as an object moves in relation to the observer. As it approaches you, the frequency decreases and the item exhibits a blueshift. A redshift indicates that an item is travelling away from us.
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A stone is thrown vertically upward with an initial speed of 18.1 m/s. Neglect air resistance. The speed of the stone when it is 8.26 m higher is:
The velocity of the object when it first reaches a height of 8.10 meters is 18.05 m/s.
Calculation-To find the speed of the stone when it is 8.26 m higher, we can use the equation for vertical motion under constant acceleration. The equation is:
v^2 = u^2 + 2as
Where:
v = final velocity (m/s)
u = initial velocity (m/s)
a = acceleration due to gravity (9.8 m/s^2, downward)
s = distance traveled (m)
In this case, the initial velocity is 18.1 m/s, the distance traveled is 8.26 m upward, and the acceleration due to gravity is 9.8 m/s^2 downward. We can substitute these values into the equation and solve for the final velocity.
v^2 = 18.1^2 + 2 * 9.8 * 8.26
v^2 = 327.61
v = sqrt(327.61)
v = 18.05 m/s
Why ignore air resistance while calculating projectile motion?Air resistance is the term for the frictional force that slows an object's velocity as it moves through the air. Although air resistance considerably affects trajectory motion, it is not taken into account in beginning physics due to the complexity of the calculations.
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When there is no motion between objects, what is the relationship between the magnitude of the static friction, f, and the normal force, N?
The static friction and the normal force are related to each other as ≤.
Static friction is a force that prevents an item from moving. The friction encountered when persons attempt to move a stationary object on a surface without actually causing any relative motion between the body and the surface on which it is located. Static friction occurs between two fixed things, whereas kinetic friction occurs when two items move. Static friction varies while kinetic friction remains constant.
The normal force is the force exerted by surfaces to prevent solid objects from passing through them. A contact force is normal force. According to Newton's third law, this force on the platform must be followed by an equal and opposite force delivered to the man by the platform. This force is identical to the normal force.
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A focus mirror sculpture was opened in Rockefeller Centre in New York City in 2006. Standing three storeys tall and weighing 23 tonnes, its concave side faced the Rockefeller Centre and its convex side faced 5th Avenue.
A. What is the nature of the image of 5th Avenue?
B. Which property of concave mirror is utilised for using them as shaving mirrors?
C. A taxi on 5th Ave is located 38 metres from the convex side of this culture and its image is 1/5 the size of the taxi. Determine the focal length of the mirror.
D. Estimate the image size of the 270 metre tall Rockefeller Centre if it is located an estimated distance of 100 metres from the concave mirrors surface of focal length 10 metre.
A. The nature of the image of 5th Avenue in the mirror sculpture is that it is a virtual, upright, and smaller image. This is because the concave mirror is used to reflect light outwards, creating a virtual image that cannot be projected onto a screen.
B. The property of concave mirrors that is utilized for using them as shaving mirrors is their ability to form a smaller, magnified image. This is because concave mirrors have a negative focal length, which causes light rays to diverge and form a smaller image that is closer to the mirror.
C. To determine the focal length of the mirror, we can use the formula 1/f = 1/u + 1/v, where f is the focal length, u is the object distance (38 meters), and v is the image distance (unknown). We know that the image size is 1/5 the size of the object, so we can set v = -5u (since the image is virtual and inverted). Substituting these values into the formula and solving for f, we get f = -(5u^2)/4 = -(5(38^2))/4 = -4725/4 = -1181.25 meters.
D. To estimate the image size of the 270 meter tall Rockefeller Centre, we can use the formula: h' = -h * (u/f) where h' is the image height, h is the object height (270 meters), u is the object distance (100 meters) and f is the focal length (10 meters). Substituting these values in the formula, h' = -270 * (100/10) = -2700 meters. This means the image of the Rockefeller Centre would be 2700 meters tall, which is not possible because it's taller than the building itself. This is an indication that the image is not real and is a virtual image.
What is the difference between flat mirrors and curved mirrors?Unlike plane mirrors, spherical mirrors form images that are different in size from the size of the object. While the convex mirror forms images that are always smaller than the object, the concave mirror forms images of different sizes, depending on the position in which the object is placed on its axis.
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