Suppose two skiers (A and B) are racing. Assume a frictionless surface! They start from the top of a mountain at the same time, and glide down to the flat area below. Just before the finish line there is a ditch. The skiers can either go down into the ditch or take a flat bridge over the ditch. Both the bridge and the ditch are covered with frictionless snow. Skier A decides to go down into the ditch. Skier B decides to go over the bridge. . Which skier gets to the finish line first, or do they arrive at the same time?
a. Skier A (ditch) arrives first
b. Skier B (bridge) arrives first
c. The skiers arrive at the same time
d. Neither skier arrives at the finish line
Answer:
b. Skier B (bridge) arrives first
Explanation:
This is because, skier B continues along the bring with the same velocity he started with before moving over the bridge and since the bridge is frictionless, he losses no kinetic energy and his speed is constant.
Whereas, skier A losses kinetic energy as he goes into the ditch. This is due to his change in potential energy. He thus emerges from the ditch with lesser kinetic energy than skier B and thus a slower speed.
Therefore, skier B arrives first since he moves at a constant speed.
Patrick the pole vaulter is running with a 20m long pole toward a 10m long garage with doors at each end. Patrick is running so fast that to an observer O in the rest frame of the garage, the pole appears only 10m long (i.e. the pole would just fit inside the garage).
a. In the frame of observer O, how fast is Patrick running?
b. The observer O closes very quickly the doors on both ends of the garage just as Patrick and the pole are inside, and then immediately opens them again so that Patrick can run out on the other end. However, according to Patrick, the garage is moving towards him and is only 5m long. How can Patrick and his 20m pole possibly make it through without hitting a door?
Answer with Explanation:
We are given that
Length of pole(l0)=20 m
Length of garage(l)=10 m
a. We have to find the speed by which the Patrick is running.
We know that
[tex]l=l_0\sqrt{1-\frac{v^2}{c^2}}[/tex]
Substitute the values
[tex]10=20\sqrt{1-\frac{v^2}{c^2}}[/tex]
[tex]\frac{10}{20}=\sqrt{1-\frac{v^2}{c^2}}[/tex]
[tex]\frac{1}{2}=\sqrt{1-\frac{v^2}{c^2}}[/tex]
[tex]\frac{1}{4}=1-\frac{v^2}{c^2}[/tex]
[tex]\frac{v^2}{c^2}=1-\frac{1}{4}=\frac{3}{4}[/tex]
[tex]v^2=0.75c^2[/tex]
[tex]v=0.87c[/tex]
b.
l0=10 m
[tex]l=10\sqrt{1-\frac{3}{4}}[/tex]
[tex]l=5m[/tex]
Hence, the length of garage appear to him=5 m long.
Use g = 9.80 m/s2 (down]
1. What velocity does a freely falling object reach after 4.0 s if it starts from rest?
The velocity of the freely falling object reached after 4.0 s is equal to 39.2 m/s.
What is the equation of motion?A relation can be established between the velocity of the body and acceleration of the body when the body is moving along a straight line with uniform acceleration. The distance traveled by the body in a specific time has expressed a set of equations called equations of motion.
The first equation of motion can be expressed as follows:
v = u + at
Where u is the initial velocity, v is the final velocity and a is the acceleration and t is the time of the object.
Given, the acceleration of the falling object, g = 9.8 m/s²
The initial velocity of the object, u = 0, and the time = 4 sec
The velocity of the object after time, t = 4 sec.
v = (0) + (9.80)× (4)
v = 39.2 m/s
Therefore, the velocity of the falling object will be 39.2 m/s after 4 seconds.
Learn more about the equation of motion, here:
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A traffic light consists of a horizontal member attached to a vertical support post. The horizontal member extends 7 m to the left of the support post and has a constant mass density of 15 kg/m. Each traffic light has mass of 10 kg, and the street sign has a mass of 4.5 kg. Make sure the connection between the horizontal member and the vertical support post is strong enough to withstand the forces exerted on the horizontal member. Calculate the effects of the forces resulting from the two traffic lights and the street sign on the horizontal member.
Answer:
τ = 539 N m
Explanation:
Let's use the rotational equilibrium relationship, where we set our reference system at the junction of the poles and the counterclockwise rotations we consider positive
τ = Σ τ_i
the mass of the traffic lights is m₁ = 10 kg, the mass of the sign m₂ = 4.5kg and suppose the worst case all the elements connected at the end (x = 7 m)
τ = 2 m₁ x + m₂ x + m₃ x / 2
we calculate the mass of the horizontal pole using the concept of linear density
λ = m₃ / l
m₃ = λ l
we substitute
τ = (2m₁ + m₂) x + λ l x / 2
τ = x (2m₁ + m₂ +λ l / 2)
let's calculate
τ = 7 (2 10 + 4.5 + 15 7/2)
τ = 539 N m
therefore, this is the torque that the joint between the two posts must resist
How do I find the specific heat?
I know that
Q= m x c x difference in T
Q= 1.61
M= 476
C=?
Difference in temperature = 20
Answer:
Hope it may help you have a great day at school bye bye. Plz put it in brainliest answer my only request plz plz plz plz plz
You and two of your friends are at the edge of a cliff. Each of you pick up a stone and throw it over the edge at the same time and with the same initial speed. One of you throws the stone at an angle above the horizon, another throws the stone horizontally, and the third throws the stone at an angle below the horizon. Rank the speed of each stone just before it hits the ground from highest to lowest.
Answer:
The speed of stone while hitting the ground in all the three cases will be same .
Explanation:
The speed of stone while hitting the ground in all the three cases will be same .
They all will have same initial kinetic energy because they have same initial speed . Kinetic energy of an object does not depend upon the direction of velocity of the object .
They will all gain kinetic energy due to loss of height .Since they all fall from the same height , gain of kinetic energy in all the three cases will also be same .
Hence final kinetic energy will be same when they hit the ground .
Hence they all have same speed while hitting the ground .
Michelle and Isabella are ice skating together. Michelle has a mass of 80 kg and Isabella has a mass of 50 kg. Both are at rest and and Isabella pushes of Michelle causing Isabella to move away at a speed of 4.0 m/s. Determine Michelle's speed.
Answer:
2.5 m/s
Explanation:
We assume the skates are positioned so that the motion is essentially frictionless.
Conservation of momentum tells you Michelle's velocity (v) must satisfy ...
∑mv = 0
(80 kg)(v) + (50 kg)(4 m/s) = 0
v = -(50 kg)(4 m/s)/(80 kg) = -2.5 m/s
Michelle's speed is 2.5 m/s in the direction opposite Isabella's.
Answer:
2.5 m/s
Explanation:
A cube has a density of 1800 kg/m3 while at rest in the laboratory. What is the cube's density as measured by an experimenter in the laboratory as the cube moves through the laboratory at 89.0 % of the speed of light in a direction perpendicular to one of its faces?
Answer:
3947.7 kg/m³
Explanation:
The relativistic density can be calculated using below expression;
ρ = ρ' /[√( 1 - v²/c²)]
where,
ρ = Change in Density as a result of motion
ρ'= Actual density of cube
ρ' is given as = 1800 kg/m³
v = Velocity that the cube moves = 0.89c
c = Speed of light
c= 3×10^8 m/s
ρ = ρ' /[√( 1 - v²/c²)]
if we substitute the given values we have
ρ= 1800/ √ 〈1- 0.89c²/ c²〉
ρ=3947.7 kg/m³
Hence, the cube's density is 3947.7 kg/m³
PLEASE HURRY Take 40 points.please just look at the picture.
Answer:
It you get a sushi for work, for a party, then it leads to people being happy, as an independant variable
It is changing the molecular structure of a protein
Explanation:
Modify how could you charge the electric circuit shown below to allow lightbulb a to stay lit even if lightbulb b is removed from its base?
Which electrons are transferred in an ionic bond?
Answer:
electrons are completely transferred from one atom to another. In the process of either losing or gaining negatively charged electrons, the reacting atoms form ions. The oppositely charged ions are attracted to each other by electrostatic forces, which are the basis of the ionic bond.
Explanation:
As you sit in a fishing boat, you noticed that 22 waves pass the boat every 60 seconds . If the distance from one crest to the next is 0.5 m, what is the speed of these waves?
Answer:
0.1835m/s
Explanation:
The formula for calculating the speed of wave is expressed as;
v = fλ
f is the frequency - The number of oscillations completed in one seconds
If 22 waves pass the boat every 60 seconds,
number of wave that passes in 1 seconds = 22/60 = 0.367 waves
Therefore the frequency f of the wave is 0.367Hertz
λ (wavelength) is the distance between successive crest and trough of a wave
λ = 0.5m
Substitute the given values into the formula
v = fλ
v = 0.367 * 0.5
v = 0.1835
Hence the speed of the waves is 0.1835m/s
Couldn’t you technically make infinite speed by putting a car in a vacuum chamber? Since top speed it made by the amount of force it takes until power and wind balance couldn’t you just get rid of that factor entirely?
Answer:
No
Explanation:
For infinite speed to be achevied, one must have no sink of energy to spend. The source of entropy in this example, is the tires hitting the surface, producing heat and friction. Not to mention that you'd still need fuel to start the car, and an infinite tunnel or track, which would be impossible and speed up to process of energy loss through entropy quicker.
define stress engineering science
Answer:
Stress, in physical sciences and engineering, force per unit area within materials that arises from externally applied forces, uneven heating, or permanent deformation and that permits an accurate description and prediction of elastic, plastic, and fluid behaviour.
I hope it's helpful!
A resistor has a power output of 15 W. If it is powered by 3 AA batteries, what is the current through the circuit?
A torch takes two 1.5 V AA batteries and provides a current of 0.3 A to the bulb. What is the power output of the bulb?
Answer:
well i am sure you need this to so look really hard at this then delete it
Explanation:
1. The speed with which electrons move through a copper wire is typically 10-4 m s-1
.
a. Explain why is it that the electrons cannot travel faster in the conductor?
b. Explain why the electron drift produces heat?
1. a) collisons with the crystal lattice atoms b) collisions with lattice atoms transfers energy.
2. Explain in terms of atomic and electron movement, why resistance increases with temperature.
2. Electrons drift through the lattice, as temperature increases the lattice atoms vibrate more and this increases the probability of
collision and hence resistance to electrons has increased.
3. Calculate the resistance of an aluminum (ρ = 2.8x10-8 Ωm) wire that is 2.0 m long and of circular cross section
with a diameter of 1.5 mm.
3. 32 mΩ
4. Determine the length of tungsten (ρ = 5.6x10-8 Ωm) wire with a diameter of 1.0 mm that is used to make a 20.0 Ω resistor.
4. 280 m
5. A nichrome (ρ = 100x10-8 Ωm) wire has a diameter of 0.40 mm. Calculate the length of this wire needed to carry a current
of 30 mA when there is a potential difference of 12 V across it.
5. 50 m
6. A thin copper (ρ = 1.68x10-8 Ωm, but you don’t need it) wire 200 cm in length has a 9 V dry cell connected between its ends.
Determine the voltage drop that occurs along 30 cm of this wire.
6. 1.35 V
7. If the potential difference across the bulb in a camping lantern is 9.0 V, what is the potential difference across the battery used to
power it?
battery gives the voltage of 9.0 V to the lantern to use it.
8. How much current, in amperes, is in a lightning stroke that lasts 0.05 second and transfers 100 coulombs?
I = q/t = (100 C)/(0.05 s) =2000 A
9. Calculate the resistance of the filament in a light bulb that carries 0.4 A when 3.0 V is impressed across it.
V = IR R = V/I = 7.5 Ω
10. Electric socks, popular in cold weather, have a 90-ohm heating element that is powered by a 9-volt battery.
How much current warms your feet?
V = I/R = 0.1 A
11. Calculate the current of a lightning bolt that delivers a charge of 35 coulombs to the ground in a time of 1/1000 second.
11. I = q/t = 35 000 A.
12. Calculate the current where 10 coulombs of charge pass a point in 5 seconds.
12. I = V/R = 2 A
13. Two light bulbs designed for 120-V use are rated at 40W and 60W. Which light bulb has the greater filament resistance? Why?
13. More current flows in the 60-W bulb, which means the resistance of the filament is less.
P = IV = V2/R, R = V2/P = (120 V)2/(60 W) = 240 Ω; for the 40-W lamp, R = (120 V)2/(40 W) = 360 Ω
14. A battery does 18 joules of work on 3 coulombs of charge. What voltage does it supply?
14. V= E/q= (18 J)/(3 C) = 6V
15. A power line with a resistance of 2 ohms has a current of 80 A in it. The power dissipated in the line is
15. 12800 W.
2
16. A toaster oven is plugged into an outlet that provides a voltage difference of 120 V.
What power does the oven use if the current is 10A?
16. P = IV = 1200 W
17. A VCR that is not playing still uses 10.0 W of power. What is the current if the VCR is plugged into a 120 V electric outlet? 17.
17. P = IV I = P/V = 0.083 A
18. A flashlight bulb uses 2.4 W of power when the current in the bulb is 0.8 A. What is the voltage difference?
18. P = IV V = P/I = 3V
19. A refrigerator operates on average for 10.0 h a day. If the power rating of the refrigerator is 700 W, how much electrical energy
does the refrigerator use in 1 day? (make sure to convert to kW)
19. E = Pt = (0.7 kW)(10.0 h) = 7 kWhours
20. A TV with a power rating of 200 W uses 0.8 kWh in one day. For how many hours was the TV on during this day?
20. E = Pt t = E/P= 0.8 kWh/0.2 kW = 4 h
21. Calculate the voltage difference in a circuit with a resistance of 25 Ω if the current in the circuit is 0.5 A.
21. V = IR = 12.5 V
22. A current of 0.5 A flows in a 60 W light bulb when the voltage difference between the ends of the filament is 120 V.
What is the resistance of the filament?
22. R = V/I = 240 Ω
23. A toy car with a resistance of 20 Ω is connected to a 3 V battery. How much current flows in the car?
23. I = V/R = 0.15 A
24. The current flowing in an appliance connected to a 120 V source is 2 A. How many kilowatt-hours of electrical energy does the
appliance use in 4 h? (2 equations used & convert watts to kW)
24. E = Pt P = IV = 0.24 kW E = 0.96 kWh
25. A calculator uses 9 V battery & draws 0.1 A of current. How much power does it use?
25. P = IV = 0.9 W
26. A battery causes 250 mA to flow when it is applied to a light bulb with a resistance of 50 ohms. How much current would flow if
the same source were applied to a 12 ohm resistor?
26. voltage of the source: V = IR = 12.5 V I = V/R = 1.04 A
Newtons third law is called law of action and reaction?
Answer:
His third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A. ... In reaction, a thrusting force is produced in the opposite direction.
Explanation:
Answer:
These two forces are called action and reaction forces and are the subject of Newton's third law of motion Formally stated Newton's third law is For every action
Explanation:
Microtubules are filamentous structures in cells that maintain cell shape and facilitate the movement of molecules within the cell. They are long, hollow cylinders with a diameter of about 25 nm. It is possible to incorporate fluorescent molecules into microtubules; when illuminated by an ultraviolet light, the fluorescent molecules emit visible light that can be imaged by the optical system of a microscope.
Required:
If the emitted light has a wavelength of 550nm and the NA of the microscope objective is 1.3, what is the smallest resolvable separation between two objects in the microscope?
Answer:
the smallest resolvable separation between two objects in the microscope is 2.58 × 10⁻⁷ m
Explanation:
Given the data in the question;
the smallest resolvable separation distance between two objects in the microscope can be determined using the following quation;
[tex]d_{min}[/tex] = Dλ/NA = (0.61)λ /NA
where λ is the wavelength of emitted light = 550nm = 5.5 × 10⁻⁷ m
NA = microscope objective = 1.3
so we substitute
[tex]d_{min}[/tex] = (0.61)5.5 × 10⁻⁷ m) / 1.3
[tex]d_{min}[/tex] = 0.0000003355 / 1.3
[tex]d_{min}[/tex] = 2.58 × 10⁻⁷ m
Therefore, the smallest resolvable separation between two objects in the microscope is 2.58 × 10⁻⁷ m
A woman stands on a moving sidewalk (conveyor belt) that is moving to the right at a speed of 2 m/s relative to the ground. A dog runs on the belt toward the woman at a speed of 8 m/s relative to the belt. A conveyor belt is moving to the right at the speed v subscript belt, ground equals 2 meters per second. A girl stands stationary on the left end of the belt. A dog runs on the belt to the left toward the girl at the speed v subscript dog, belt equals 8 meters per second. What is the speed of the dog relative to the ground
Answer:
V_{2G} = - 10 m / s
Explanation:
This is an exercise on relative velocities in one dimension, let's use the subscript 1 for the girl, the 2 for the but, the index 3 for the conveyor belt and the index G for the Earth
we will consider the velocity is positive to the right.
They indicate the speed of the belt with respect to the ground = 2 m/s
the dog speed with respect to the belt = - 8 m / s
Dog speed is requested with respect to the Earth
[tex]V_{2G} = V_{23} - V_{3G}[/tex]
notice that the inner subscripts cancel out.
We calculate
= -8 - 2
V_{2G} = - 10 m / s
the negative sign indicates that the dog moves to the left
Explain why objects in water appear to be a different size then the same objects above the water.
Answer:
the answer is the third one since water reflects it
Explanation:
A train 350 m long is moving on a straight track with a speed of 84.1 km/h. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 15.8 km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.
Answer:
t = 25.0 s
Explanation:
Assuming that the engineer applies the brakes just over the crossing, the train moves exactly 350 m at a constant acceleration, with a final speed (when the last car of the train leaves the crossing) of 15.8km/h.Since we know the initial and final speeds, and the horizontal distance traveled (the length of the train) we can use the following kinematic equation to get the acceleration:[tex]v_{f}^{2} - v_{o}^{2} = 2*a* \Delta x (1)[/tex]
Since we need to find the time in seconds, it is advisable to convert vf and vo to m/s first, as follows:[tex]v_{o} = 84.1 km/h*\frac{1h}{3600s} *\frac{1000m}{1km} = 23.4 m/s (2)[/tex]
[tex]v_{f} = 15.8 km/h*\frac{1h}{3600s} *\frac{1000m}{1km} = 4.4 m/s (3)[/tex]
Replacing (2) and (3) in (1), since Δx =350m, we can solving for a:[tex]a = \frac{(4.4m/s)^{2} - (23.4m/s)^{2}}{2*350m} = -0.76 m/s2 (4)[/tex]
In order to get the time, we can simply use the definition of acceleration, and rearrange terms:[tex]t =\frac{v_{f}-v_{o}}{a} = \frac{(4.4m/s)-(23.4m/s)}{-0.76m/s2} = 25.0 s (5)[/tex]
Anita is bouncing a tennis ball on the sidewalk. She drops the ball and then watches it bounce back up. At which point does Anita's tennis ball have zero kinetic energy?
A
as it hits the sidewalk's surface
B
just after it hits the sidewalk's surface
С
as it begins to fall to the sidewalk
D
just as it reaches the top of the bounce
Answer:
Just as it reaches the top of the bounce.
Explanation:
When an object reaches to the maximum height, its kinetic energy is equal to 0. It can be calculated as follows :
[tex]K=\dfrac{1}{2}mv^2[/tex]
Where
m is mass and v is velocity
In this problem, Anita is bouncing a tennis ball on the sidewalk. She drops the ball and then watches it bounce back up.
It means, when it reaches the top of the bounce, Anita's tennis ball have zero kinetic energy. Hence, the correct option is (d).
A fox locates its prey under the snow by slight sounds rodents make. The fox then leaps straight into the air, and then burrows its nose into the snow to catch its meal. If a fox jumps up to a height of 79 cm, calculate (a) the speed at which the fox leaves the snow, and (b) how long the fox is in the air. Ignore air resistance.m/s:s:You throw a baseball directly upward at time t = 0 at an initial speed of 12.9 m/s. What is the maximum height the ball reaches above where it leaves your hand? At what times does the ball pass through half the maximum height? Ignore air resistance and take g = 9.80 m/s2.Maximum height:Earlier time at half maximum height:Later time at half maximum height:
Answer:
1.a) 3.93 m/s
b) 0.80 s
2. a) 8.49 m
b) 0.39 s
Explanation:
1. a) The speed at which the fox leaves the snow can be found as follows:
[tex] v_{f}^{2} = v_{0}^{2} - 2gH [/tex]
Where:
g: is the gravity = 9.80 m/s²
[tex]v_{f}[/tex]: is the final speed = 0 (at the maximum height)
[tex]v_{0}[/tex]: is the initial speed =?
H: is the maximum height = 79 cm = 0.79 m
[tex] v_{0} = \sqrt{2gH} = \sqrt{2*9.80 m/s^{2}*0.79 m} = 3.93 m/s [/tex]
Hence, the speed at which the fox leaves the snow is 3.93 m/s.
b) The time at which the fox reaches the maximum height is given by:
[tex]v_{f} = v_{0} - gt[/tex]
[tex]t = \frac{v_{0} - v_{f}}{g} = \frac{3.93 m/s}{9.80 m/s^{2}} = 0.40 s[/tex]
Now, the time of flight is:
[tex] t_{v} = 2t = 2*0.40 s = 0.80 s [/tex]
2. a) The maximum height the ball reaches is:
[tex] H = \frac{v_{0}^{2} - v_{f}^{2}}{2g} = \frac{(12.9 m/s)^{2}}{2*9.80 m/s^{2}} = 8.49 m [/tex]
Then, the maximum height is 8.49 m.
b) The time at which the ball passes through half the maximum height is:
[tex]y_{f} = y_{0} + v_{0}t - \frac{1}{2}gt^{2}[/tex]
Taking y₀ = 0 and [tex]y_{f}[/tex] = 8.49/2 = 4.245 m we have:
[tex] 4.245 m -12.9m/s*t + \frac{1}{2}*9.80m/s^{2}*t^{2} = 0 [/tex]
By solving the above quadratic equation we have:
t = 0.39 s
Therefore, the time at which the ball passes through half the maximum height when the ball is going up is 0.39 s.
I hope it helps you!
An upward force of 32.6 N is applied via a string to lift a ball with a mass of 2.8 kg. (a) What is the gravitational force acting on the ball? (b) What is the net force acting upon the ball? (c) What is the acceleration of the ball?
Answer:
a) Fg = -27.4 N
b) Fnet = 5.2 N
c) a = 1.9 m/s2
Explanation:
a)
There are two forces acting on the ball, one directed upward (assuming this direction as positive, along the y-axis) which is the tension on the string (lifting force), and another aimed downward, which is the attractive force due to gravity.Applying the Newton's Universal Law of Gravitation to a mass close to the surface of the Earth (in this case the ball), we can take the acceleration due to gravity like a constant, that we call by convention g, equal to -9.8 m/s2.So, we can write the following expression for Fg:[tex]F_{g} = m*g = 2.8 kg*(-9.8m/s2) = -27.4 N (1)[/tex]
b)
The net force on the ball, will be just the difference between the lifting force (32.6 N) and the force due to gravity, Fg:[tex]F_{net} = T -F_{g} = 32.6 N - 27.4 N = 5.2 N (2)[/tex]
c)
According Newton's 2nd Law, the acceleration caused by a net force on a point mass (we can take the ball as one) is given by the following expression:[tex]a = \frac{F_{net} }{m} = \frac{5.2N}{2.8kg} = 1.9 m/s2 (3)[/tex]
models are frequently used in science to assist in the understanding of complex information. Models can include items like a working volcano, and aquarium, or a stream table. What type of model are each of these items?
A) two dimensional
b) three dimensional
c) mental explanation
d) Computer simulation
If the mass of a basketball is 18 times that of a tennis mass, can they ever have the same momentum? Explain your answer
Answer:
Yes
Explanation:
Yes. The momentum is the same when the speed of the tennis ball is 18 times greater than the speed of the basketball and the velocities of both objects are in the same direction.
A rock thrown vertically upward from the surface of the moon at a velocity of 32m/sec reaches a height of sequals32 t minus 0.8 t squaredmeters in t sec.a. Find the rock's velocity and acceleration at time t.b. How long does it take the rock to reach its highest point?c. How high does the rock go?d. How long does it take the rock to reach half its maximum height?e. How long is the rock aloft?
Answer:
A) v(t) = (32 - 1.6t) m/s
a(t) = -1.6 m/s²
B) t = 20 seconds
C) 320 m
D) t = 5.85 seconds going up and 34.14 seconds going down
E) 40 seconds
Explanation:
Height is given by the equation;
S(t) = 32t - 0.8t²
A) Velocity after time t is gotten from first derivative of the distance.
Thus;
v(t) = dS/dt = 32 - 1.6t
Acceleration at time t is gotten from derivative of the velocity.
Thus;
a(t) = d²S/dt² = -1.6 m/s²
B) At highest point, velocity is zero.
Thus;
32 - 1.6t = 0
1.6t = 32
t = 32/1.6
t = 20 seconds
C) To find how high the rock goes, it means we are looking for maximum height.
This will be at t = 20 seconds.
Thus;
S(20) = 32(20) - 0.8(20)²
S(20) = 640 - 320
S(20) = 320 m
D) we want to find the time it will take to reach half its maximum height.
since maximum height is 320 m, then half the maximum height is; S_½ = 320/2 = 160
Thus;
160 = 32t - 0.8t²
0.8t² - 32t + 160 = 0
Using quadratic formula, we will get;
t = 5.85 seconds going up and 34.14 seconds going down
E) time the rock is aloft = twice the time it took to reach maximum height.
Thus; t_aloft = 2 × 20 = 40 seconds
You want to see how your new belt buckle matches your new hat. Your eyes are 114 mm below the top of the hat and 800 mm above the buckle. You walk up to your mirror and notice that the mirror is exactly large enough and exactly in the right position for you see both the top of the hat and the buckle.
1. What is the position of the top edge of the mirror relative to your eyes?2. How tall is the mirror?
Answer:
[tex]x=0.057m[/tex]
[tex]h=0.457m[/tex]
Explanation:
From the question we are told that
Distance of eyes from the top of hat [tex]d_1=114mm[/tex]
Distance of eyes from buckle [tex]d_2=800mm[/tex]
Generally position of mirror relative eyes x is mathematically given as
[tex]x=\frac{114}{2}[/tex]
[tex]x=57mm[/tex]
[tex]x=0.057m[/tex]
Generally the height of the mirror h is mathematically given as
[tex]h=\frac{(Buckle\ below\ the\ hat)+(Buckle\ below\ the\ hat)}{2}[/tex]
[tex]h=\frac{(114)+(800)}{2}[/tex]
[tex]h=457mm[/tex]
[tex]h=0.457m[/tex]
a star produces energy by? ( a p e x )
A. absorbing and releasing the matter of other stars.
B. rotating quickly on its axis.
C. reflecting energy from nearby stars.
D. creating helium from hydrogen in its core.
A star produces energy by creating helium from hydrogen in its core (option D).
How does a star produce energy?A star is a luminous celestial body, made up of plasma (particularly hydrogen and helium) and having a spherical shape.
Nuclear fusion is the energy-producing process in stars. The "proton-proton chain," a series of events that turns four hydrogen atoms into one helium atom, dominates this process for the majority of stars.
Nuclear fusion is the combining of the nuclei of small atoms to form the nuclei of larger ones, with a resulting release of large quantities of energy.
Hydrogen atoms fuse in the core of the star to form a helium atom, which generates the energy for the star.
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Given that the frequency of an EM wave is 4THz, what is its wavelength?
Answer:
The wavelength of the EM wave is 7.5 * 10⁻⁴ m
Explanation:
The velocity of a wave is related to its wavelength by the following formula;
velocity = wavelength * frequency
For an electromagnetic (EM) wave, its velocity is equal to the velocity of light, c = 3.0 * 10⁸ m/s
Given that the frequency and veloity of the given EM wave in the question is known, its wavelength is calculated as follows:
wavelength = velocity/frequency
where velocity of the EM wave = 3.0 * 10⁸ m/s;
frequency = 4THz = 4 * 10¹² Hz
wavelength = 3.0 * 10⁸m/s / 4 * 10¹² Hz
wavelength = 7.5 * 10⁻⁴ m
Therefore, the wavelength of the EM wave is 7.5 * 10⁻⁴ m
Answer:
The wavelength is 7.5 x 10^-5m
Which choices describe a step in the process of oil formation?
Choose all correct answers.
1. Most organic material is recycled by microorganisms.
2. Organisms die and sink to the ocean floor.
3. Heat and pressure changes dead remains.
4. Layers of sediment cover dead remains.
The choices that represent the step in the oil formation process are:
Layers of sediment cover dead remains.
Organisms die and sink to the ocean floor.
Heat and pressure change dead remains.
Oil formation process:Oil and gas should be created from organic material that is deposited with respect to the sediments on the seabed and after that, it brokes down and then transformed over millions of years. The sediment layers should be covered and dead. The organisms die and then they sink to the ocean. The change to the heat and pressure should remain dead.
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Answer: 2, 3, and 4.
Organisms die and sink to the ocean floor.
Heat and pressure changes dead remains.
Layers of sediment cover dead remains.
Explanation:
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