The figure provided shows the production possibilities for Alabama and Georgia.a) Compared to autarky, the gain in world production from specialization is _____ bushels of peaches.b) Compared to autarky, the gain in world production from specialization is _____ bushels of tomatoes.

The velocity of the runner at t=π/2 seconds is 15 miles/hour.

The directional speed of an item in motion, as measured by a specific unit of time and viewed from a certain point of reference, is what is referred to as velocity.

The function is as follows:

f(t)=-10cos(t) + 15

The time in this case is shown as t.

We must change t=/2 in the given function to obtain the runner's speed at t=/2 seconds:

f(π/2) = -10cos(π/2) + 15

f(π/2) = -10(0) + 15

f(π/2) = 15

As a result, the runner's speed at t=/2 seconds is 15 miles per hour.

We may deduce that the runner is moving towards the north at a speed of 15 miles per hour at t=/2 seconds since f(t) > 0 denotes moving in that direction.

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The reaction rate constant and activation energy have an exponential connection, which is described by the Arrhenius equation, which may be used to predict reaction rate constants for chemical reactions as a function of temperature.

Define Q, ko, and R, as well as the other specified constants.

The "linspace" function in Matlab can be used to create a vector of temperature values ranging from 300 K to 1000 K.

Use the Arrhenius equation and the listed constants to determine the value of k for each temperature value.

Plot temperature values on the x-axis and k values on the y-axis using the Matlab "plot" function. Plot 1/T values on the x-axis and the log10 of k values on the y-axis using the same Matlab "plot" function.

Add titles to the figure window and label the x- and y-axes on both graphs.

% Define constants

Q = 1000; % J/mol

ko = 10; % s^-1

R = 8.314; % J/mol-K

% Create a vector of temperature values

T = linspace(300, 1000);

% Calculate k values using the Arrhenius equation

k = ko * exp(-Q./(R.*T));

% Create a subplot with two graphs

subplot(1, 2, 1)

plot(T, k)

xlabel('Temperature (K)')

ylabel('Reaction Rate Constant (s^-1)')

title('Arrhenius Plot')

subplot(1, 2, 2)

plot(1./T, log10(k))

xlabel('1/Temperature (1/K)')

ylabel('log10(Reaction Rate Constant)')

title('Modified Arrhenius Plot')

The Arrhenius plot and the modified Arrhenius plot are two subplots that should appear in a single figure window created by this code. The Arrhenius plot displays the correlation between temperature and the reaction rate constant, whereas the modified Arrhenius plot displays the correlation between 1/T and the log10 of the reaction rate constant.

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he minimum value of v is determined by the forces acting on the sphere. The forces acting on the sphere are gravity, tension in the wires AC and BC, and the centripetal force.

The centripetal force is equal to the product of the mass of the sphere and its velocity squared, divided by the radius of its orbit. Since the sphere is in equilibrium, these forces must be in balance. Therefore, the minimum value of v can be determined by setting the gravity force and the tension in the wires equal to the centripetal force. This gives us:

mv2/r = TAC + TBC

where m is the mass of the sphere, v is the velocity, r is the radius of the orbit, and TAC and TBC are the tensions in the wires AC and BC respectively.

Solving for v gives:

v = sqrt(TAC + TBC * (r/m))

Substituting the values given in the problem, we get:

v = sqrt((TAC + TBC) * (1.6/5))

Therefore, the minimum value of v is:

v = sqrt(TAC + TBC) = sqrt(2 * (1.6/5)) = 0.96 m/s

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The forces operating on the sphere define the minimal value of v. The sphere is subject to the forces of gravity, centripetal force, and tension in wires AC and BC.

The centripetal force is determined by multiplying the sphere's mass by its velocity squared and dividing the result by the radius of its orbit. These forces must be in balance for the sphere to be in equilibrium. As a result, the minimum value of v can be calculated by setting the centripetal force, gravity force, and wire tension to the same value. This results in:

mv2/r = TAC + TBC

where m is the mass of the sphere, v is the velocity, r is the radius of the orbit, and TAC and TBC are the tensions in the wires AC and BC respectively.

Solving for v gives:

v = sqrt(TAC + TBC * (r/m))

Substituting the values given in the problem, we get:

v = sqrt((TAC + TBC) * (1.6/5))

Therefore, the minimum value of v is:

v = sqrt(TAC + TBC) = sqrt(2 * (1.6/5)) = 0.96 m/s

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Answer: The given time period of oscillation would be around 0.9515 seconds.

Explanation:

The very first 54.0 km were driven at an average speed, while the final 86.0 km were driven at in a speed of (43.0 b) km/h. She travels at an average speed of 43.75 km/h for the entire journey.

Velocity is the pace and velocity of an object's movement, whereas speed is the forecasting at which an objects is travelling along a path. In other words, velocity is a vector, whereas quickness is a scalar value. As a result, the fundamental unit of time and the basic element of distance are combined to form the Special name of speed. Thus, the metre per second (m/s) is the Substrate concentration of speed.

a = 19 and b = 7

Average speed, 54 km = 48+a km/h

Plug a = 19

54 km = 48+19

= 67 km/h

remaining speed

86 km = 43-b km/h

where b = 7

Average speed = 36 km/h

Average speed = total distance / total time taken

speed = distance/time

time = distance/speed

To cover 54 km = 54/67 hr

To cover 86 km = 86/36 hr

Total time = 3.2 hours.

Total distance = 86+54

= 140 km

Average speed 140/3.2

= 43.75 km/ h

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The speed of the phone just before touching the ground is approximately 3.92 m/s.

We can use the conservation of energy to find the speed of the phone just before touching the ground. Initially, the phone has potential energy due to its height above the ground, which is converted into kinetic energy just before the phone touches the ground.

The potential energy of the phone just before it is dropped is:

[tex]PE = mgh[/tex]

where m is the mass of the phone, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the phone above the ground (1.50 m). Thus, the initial potential energy of the phone is:

[tex]PE = (0.65 kg)(9.81 m/s^2)(1.50 m) = 9.57 J[/tex]

As the phone is dropped, gravity does 8.80 J of work on the phone. This work is converted into kinetic energy just before the phone touches the ground. Thus, the final kinetic energy of the phone just before it touches the ground is:

[tex]KE = W = 8.80 J[/tex]

The kinetic energy of an object is given by:

[tex]KE = (1/2)mv^2[/tex]

where v is the speed of the object.

Thus, we can solve for the speed of the phone just before it touches the ground:

[tex]v = sqrt(2KE/m) = sqrt(2(8.80 J)/(0.65 kg)) = 3.92 m/s[/tex]

Therefore, the speed of the phone just before touching the ground is approximately 3.92 m/s.

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(a) The elevator is be moving upwards and accelerating upwards.

(b) The acceleration of the student is 0.5 m/s².

The net force acting on the elevator is determined by applying Newton's second law of motion as shown below.

F (net) = Ws + We ( when the elevator is moving upwards )

F (net) = Ws - We ( when the elevator is moving downwards)

where;

Since the resultant force of the elevator is greater than the weight of the student, the elevator must be moving upwards.

The mass of the student = 600 N / 9.8 m/s² = 61.22 kg

The acceleration of the student = ( 630  N - 600 N ) / ( 61.22 kg )

= 0.5 m/s²

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Part A

The angular separation of the two stars is 0.03 degrees

Part B

The angular separation of the two stars is 108 arcseconds.

Part C

Yes, the Hubble Space Telescope can resolve the two stars.

Angular separation is the angular distance between two objects as seen from a particular point in space. This is usually expressed in degrees, arcminutes, or arcseconds. It is a measure of the angular separation between two objects, such as stars, planets, galaxies, or other celestial objects, as seen from Earth. The angular separation of two objects is the angle between them as seen from the observer's point of view.

For example, the Moon and the Sun have an angular separation of 0.5 degrees when they are in opposition.

Part A:

To find the angular separation of the two stars, we can use the formula:

θ = arctan(d/D)

where θ is the angular separation, d is the physical distance between the two stars, and D is the distance to the stars from Earth.

Substituting the given values, we get:

θ = arctan(100,000,000 km / (200 x 9.461 trillion km))

θ = arctan(100,000,000 km / 1.8922 x 10^15 km)

θ = 0.03 degrees

Therefore, the angular separation of the two stars is 0.03 degrees.

Part B:

To convert degrees to arcseconds, we can use the formula:

1 degree = 3600 arcseconds

Substituting the value we found in part A, we get:

θ = 0.03 degrees x 3600 arcseconds/degree

θ = 108 arcseconds

Therefore, the angular separation of the two stars is 108 arcseconds.

Part C:

To determine if the Hubble Space Telescope (HST) can resolve the two stars, we need to compare the angular separation of the stars to the angular resolution of the HST. The angular resolution of a telescope is the smallest angle between two point sources that the telescope can distinguish.

The angular resolution of the HST is about 0.05 arcseconds. Since the angular separation of the two stars is 108 arcseconds, the HST can easily resolve the two stars as separate objects.

Therefore, the HST can resolve the two stars in the binary star system.

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Answer:

Explanation:

when gravity pulls the water molecules downwards, they will fall. But if they're in a container, the container will keep them from spreading out completely. This is what's called 'taking the shape of the container'

To make the program run two times faster, we need to improve the CPI of FP instructions from 1 to 5.859375.

To determine the execution time of the program, we can use the following formula:

Execution Time = (Number of Instructions x CPI) / Clock Rate

We can calculate the total number of instructions as follows:

Total Instructions = 50 * 10⁶ FP instructions + 110 * 10⁶ INT instructions + 80 * 10⁶ L/S instructions + 16 * 10⁶ branch instructions

Total Instructions = 256 x 10⁶ instructions

We can calculate the current CPI for the program as follows:

CPI = (50 * 1 + 110 * 1 + 80 * 4 + 16 * 2) / 256

CPI = 1.8125

We can calculate the current execution time of the program as follows:

Execution Time = (256 * 10⁶ * 1.8125) / (2 * 10⁹)

Execution Time = 0.29296875 seconds

To make the program run two times faster, we need to reduce the execution time to 0.146484375 seconds. We can use the same formula to calculate the new CPI for the FP instructions:

New CPI = (Execution Time x Clock Rate) / (Number of Instructions x 2)

We can rearrange the formula to solve for the new CPI:

New CPI = (Execution Time x Clock Rate) / (Number of Instructions x 2)

New CPI = (0.146484375 * 2 * 10⁹) / (50 * 10⁶ * 1)

New CPI = 5.859375

To make the program run two times faster, we need to improve the CPI of FP instructions from 1 to 5.859375. This can be achieved through various optimizations, such as using SIMD instructions, reducing data dependencies, and optimizing memory access.

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The correct answer is C. -3 nC.

When a charge is placed inside a hollow cavity of metal, the metal will rearrange its charges to cancel out the charge inside the cavity. This means that the exterior surface of the metal will have a charge opposite to the charge inside the cavity.

In this case, since the charge inside the cavity is +3 nC, the charge on the exterior surface of the metal will be -3 nC. This is known as the principle of charge neutrality.

Therefore, when a charge of +3nC is placed in a hollow cavity inside a large chunk of metal that is electrically neutral, the total charge on the exterior surface of the metal is C. -3 nC.

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Both a prism and a diffraction grating can be used to disperse white light into its component colors, which are a range of wavelengths of visible light.

θ = sin^(-1) (-1)

[n avg] = [(n blue - n red) sin()]

Assuming an angle and the values given as n red = 1.52, n blue = 1.53, and n avg = (n red + n blue)/2 = 1.525

of incidence of 45 degrees, we can calculate the angle of deviation to be:

θ = sin^(-1)[(1.53 - 1.52) sin(45°) / 1.525] = 0.34°

Therefore, the angular separation between red and blue light leaving the prism is 0.34 degrees.

nλ = d(sin θ_i + sin θ_d)

where n is the order of the diffraction (usually n=1), λ is the wavelength of the light, d is the spacing between the grating lines, θ_i is the angle of incidence of the light on the grating, and θ_d is the angle of diffraction.

θ_red = sin^(-1)[(nλ_red / d) - sin(θ_i)] = sin^(-1)[(1650 nm / 500 nm) - sin(0°)] = 0.837°

θ_blue = sin^(-1)[(nλ_blue / d) - sin(θ_i)] = sin^(-1)[(1450 nm / 500 nm) - sin(0°)] = 0.579°

Therefore, the angular separation between red and blue light leaving the grating is:

θ_separation = θ_red - θ_blue = 0.837° - 0.579° = 0.258°

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A blackbody is a hypothetical object that absorbs all incident radiation without reflecting or scattering any of it.

A blackbody is a hypothetical object that emits all wavelengths of radiation while simultaneously absorbs all electromagnetic waves that strike it.

Another name for it is a perfect emitter or absorber.

Blackbody radiation is the specific spectral distribution of radiation produced by a blackbody that is only temperature dependant.

Understanding the behaviour of thermal radiation and the properties of stars, galaxies, as well as other celestial objects in physics and astronomy is dependent on this concept.

Planck's law, which gives the spectral density of a radiation emitted by the a blackbody at a temperature t as a function of the wavelength of the radiation, describes the radiation released by a blackbody as being solely dependent on its temperature.

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The worker can load {500/ρ} number of bricks into the van.

Mass is the total amount of matter present inside a body.

Given is that a worker wants to load some bricks in to his van. There are 1000 bricks and when stacked neatly they measure 2m by 1m by 1m.

Assume the density of the brick to be {ρ}. Let's assume that he can load {n} bricks inside the van. So, we can write -

n x mass of 1 brick = maximum load

n x ρ x V = L{max}

nρV = L{max}

n = L{max}/ρV

n = 1000/(2 x 1 x 1 x ρ)

n = 500/ρ

Therefore, the worker can load {500/ρ} number of bricks into the van.

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From the height of 58.91 m would a car have to fall in order for the magnitude of its momentum to equal the magnitude of its momentum when it is moving on a highway at 34 m/s.

A motion of an item is said to have momentum when its mass multiplied by its speed. If you describe anything as having momentum, you are describing its mass and direction of motion. A truck loaded with products has a big mass and must slow down before a stop signal since stopping is exceedingly difficult due to the truck's enormous momentum and constant speed. Even though a bullet has a relatively little mass and a very high velocity, it nevertheless possesses a significant amount of momentum.

Magnitude of momentum of car on highway = m × 34 kg.m/sec

Here, mass remains the constant, speed of the car should be = 34

Thus, v² = v₀² = 2gd

v₀ = 0

v = 34 m/sec

so, d = v² /2g

d = (34)² / 2 × 9.81

d = 58.91 m

From the height of 58.91 m would a car have to fall in order for the magnitude of its momentum to equal the magnitude of its momentum when it is moving on a highway at 34 m/s.

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The potential at the center of the square is 507 V. Option (a) is correct answer.

The electric potential at a distance r from a point charge q is given by:

V = kq/r

where k is the Coulomb constant.

In this case, the charges q₂ and q₄ are negative, so the potentials due to these charges will be negative. The charges q₁ and q₃ are positive, so the potentials due to these charges will be positive. The potential at the center of the square is given by:

[tex]V = \dfrac{kq_1}{a} + \dfrac{kq_2}{\sqrt{2}a} + \dfrac{kq_3}{a} + \dfrac{kq_4}{\sqrt{2}a}[/tex]

Plugging in the values of the charges and the distance a, we get:

[tex]V = \dfrac{9 \times 10^9 \times 1 \times 10^{-8}}{1} + \dfrac{9 \times 10^9\times -2\times 10^{-8}}{\sqrt{2}\times 1} + \dfrac{9 \times 10^9\times 3 \times 10^{-8} }{1} + \dfrac{9 \times 10^9 \times 2 \times 10^{-8} }{\sqrt{2} \times 1}[/tex]

Simplifying this expression,

V = 507 V

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--The complete question is, Four point charges q1 ,q2 ,q3 and q4 are placed at the corners of the square of side a, as shown in figure. The potential at the centre of the square is: (Given: q1 =1×10^−8 C , q2 =−2×10^−8 C, q3 =3×10^−8 C, q4 =2×10^−8C, a=1m).

a. 507 V

b. 607 V

c. 550 V

d. 650 V--

Answer: F = ma = 1000 * 6.25 = 6,250 N.

Explanation:

The centripetal acceleration (a) of an object moving in a circular path is given by:

a = v^2 / r

where v is the tangential velocity and r is the radius of the loop.

The force factor, or centripetal force (F), required to keep an object moving in a circular path is given by:

F = ma

where m is the mass of the object.

At the bottom of the loop, where the tangential velocity is 10 m/s, the centripetal acceleration is:

a = v^2 / r = 10^2 / 9 = 100 / 9 m/s^2

The force factor required to maintain this acceleration depends on the mass of the object. For example, if the mass of the roller coaster car is 1000 kg, then the force factor required would be:

F = ma = 1000 * (100 / 9) = 11,111 N

At the top of the loop, where the tangential velocity is 7.5 m/s, the centripetal acceleration is:

a = v^2 / r = 7.5^2 / 9 = 6.25 m/s^2

Using the same mass of 1000 kg, the force factor required would be:

F = ma = 1000 * 6.25 = 6,250 N.

The electric field at the point (3.0 m, 2.0 m) is (4.0 V/m^2) i + (6.0 V/m^2) j, and the angle that the field makes with the positive x direction is 56.3°.

To find the electric field at a point in an xy plane, we can take the negative gradient of the electric potential at that point:

E = -∇V

where ∇ is the gradient operator. In two dimensions, the gradient operator is:

∇ = i(∂/∂x) + j(∂/∂y)

where i and j are the unit vectors in the x and y directions, respectively.

Taking the partial derivatives of V with respect to x and y, we get:

(∂V/∂x) = -4.0 V/m^2 x

(∂V/∂y) = -6.0 V/m^2 y

Substituting these into the expression for the electric field, we get:

E = -i(∂V/∂x) - j(∂V/∂y)

E = 4.0 V/m^2 i + 6.0 V/m^2 j

Now we can substitute the given values of x and y to find the electric field at the point (3.0 m, 2.0 m):

E = 4.0 V/m^2 i + 6.0 V/m^2 j

= (4.0 V/m^2)(1.0 i) + (6.0 V/m^2)(1.0 j)

= (4.0 V/m^2)(cosθ i + sinθ j)

where θ is the angle that the electric field makes with the positive x direction. To find θ, we can take the arctangent of the y component divided by the x component:

θ = tan^-1(6.0/4.0)

= 56.3°

Therefore, the electric field at the point (3.0 m, 2.0 m) is (4.0 V/m^2) i + (6.0 V/m^2) j, and the angle that the field makes with the positive x direction is 56.3°.

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The power of the pump is its work done by time. The power used  for a work done of 800 Nm in 50 seconds is 16 J/s or W. The force acting here is 40 N. Then the mass of the body is 4 kg.

Power of an object is the rate of work done or energy used.

power = work done/ time.

It has the unit watt which is equal to J/s.

a. Given work done by the pump  = 800 Nm

time = 50 s

then power = 800 Nm or J / 50 s  = 16 Watt.

b. Force F = Work done/ distance

F = 800 Nm/20 m = 40 N

c. Then force = m a

given acceleration a = 10 m/s²

m = f/ a

   = 40 N/10 m/s²

   = 4 kg.

Therefore, mass of the pump is 4 kg.

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The ranking of the energy that is requires is;

4 > 3 > 2> 1

Atomic energy levels refer to the specific energy states that an electron can occupy in an atom. Electrons in an atom can only occupy certain energy levels, and the energy levels are quantized, meaning that only specific values are allowed.

When an electron absorbs energy, it can jump to a higher energy level, and when it releases energy, it drops to a lower energy level. The energy levels are determined by the properties of the atom, such as the number of protons and neutrons in the nucleus and the electrons' distribution in the atom's electron shells.

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The following values are given: m1 = € kg, resistor = y1 Means 3.00 m, sq.m = 1.75 kg, r2 / y2. = 1.75 m, m3 = 3.00 metric tons, r3 = restrictions that limit. = 4.00 m, and = 1.75 rad/s about x-axis = m1r. 2.

The combined translational and rotational kinetic energies of an object in motion determine its total kinetic energy. 12 mvCM2 is the translational kinetic energy. Rotational kinetic energy is equal to 12 I2. Total kinetic energy is 12mvCM2 plus 12I2.

E s = x 2 x I ω 3 . . This equation shows that its kinetic energy of such a rotating solid body is inversely related to the cube of the angular acceleration and the moment of inertia. Flywheel energy-storage systems, which are intended to, take advantage.

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The required period of the function is calculated to be 1/440 sec and frequency is calculated to be 440 hertz.

The equation of the sinusoidal wave is given as, y = 0.001 sin 880πt

Comparing the given equation with that of the general equation of the wave in simple harmonic motion, we have, y = a sin ωt

where,

y is displacement

a is amplitude

t is time

ω is angular frequency

So, Angular frequency ω = 880π

The period of the function is given by the formula, p = 2π/ω = 2π/880π = 1/440 sec

We know the equation for frequency as, f = 1/p = 1/(1/440) = 440 hertz

Thus, the period of the function is 1/440 sec and frequency is calculated to be 440 hertz.

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density is the mass of a specific material per unit volume. d = M/V, in which d is densities, M is mass, as well as V is volume, is the formula for density. Common units for expressing density are grams per cubic inch.

What is the mass unit?

 There are several ways to measure mass, including kilograms, grams, pounds, and pounds, but the SI unit de mass is the "kilogram" or kg. Using the right conversion formula, any unit of weight can be changed into another unit without changing the significance or meaning of the quantity being measured.

Describe mass.

Definition, Units, Formula, and Examples of Mass The quantity of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, an chair, your mattress, a ball, a tumbler, and even air. The mass of a thing determines whether it is light or heavy.

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The gravitational force acting on satellite at an altitude R causes the centripetal acceleration it required.

Thus,  (2R) 2 GMm = 2Rmv 2

The required speed to do this—known as the circular satellite velocity—is around 8 kph, or 17,500 mph in more commonly used quantities. See how gravity affects the orbits of the Earth, Moon, and International Space Station in this additional PhET interactive.

While elliptically circling the planet, a satellite will accelerate as its height (or distance from the world) decreases and decelerate as its height (or distance from the earth) increases.

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The speed of the cars right after the collision is 1/3 m/s.

To solve this problem, we can apply the law of conservation of momentum, which states that the total momentum of a system remains constant if there are no external forces acting on it. In this case, the two railroad cars form a closed system, and there are no external forces acting on them during the collision. Therefore, we can write:

(m1 * v1) + (m2 * v2) = (m1 + m2) * v

where m1 and v1 are the mass and velocity of the first railroad car, m2 and v2 are the mass and velocity of the second railroad car, m1 + m2 is the total mass of the system after the collision, and v is the velocity of the system after the collision.

Plugging in the given values, we get:

(1500 kg * 4 m/s) + (3000 kg * (-3 m/s)) = (1500 kg + 3000 kg) * v

Simplifying and solving for v, we get:

v = (1500 kg * 4 m/s - 3000 kg * (-3 m/s)) / (1500 kg + 3000 kg)

v = (6000 kgm/s + 9000 kgm/s) / 4500 kg

v = 15/45 m/s = 1/3 m/s

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Epicycles and deferents were used to account for the planets' irregular orbital speeds in order to explain how they moved in the night sky.

A planet moves in a circle that has a core that is also rotated simultaneously on the rim of a wider circle, according to an early theory of astronomy.

Ptolemy was forced to develop a model of planetary motion that utilised epicycles in order to maintain the geocentric cosmology of the time and account for Mars' retrograde motion. An epicycle is essentially a small "wheel" that revolves around a larger wheel.

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Answer:

Explanation:

cohesion

The required speed with which the pebble strikes the ground when the pebble is fired from the slingshot with specified initial velocity is calculated to be 29.53 m/s.

The initial speed of the pebble with which it is fired is 15 m/s.

The height of the building is given as 33 m.

Acceleration due to gravity g = 9.8 m/s²

Now, let us calculate the velocity of the pebble with which it strikes the ground.

The suitable equation of motion is, v² - u² = 2 a s

where,

v is final velocity

u is initial velocity

a is acceleration

s is distance

Entering the values into the above equation by making v as subject, we have,

v² - u² = 2 a s

v² = u² + 2 a s

v = √(u² + 2 a s) = √[15² + 2(9.8)(33)] = √(225 + 646.8) = √871.8 = 29.53 m/s

Thus, the final velocity is calculated to be 29.53 m/s.

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The cannon has more mass than the ball.

option A is the correct answer.

The recoil of a cannon after firing a cannonball is a consequence of the conservation of momentum. According to this principle, the total momentum of a closed system is conserved, which means that the momentum of the cannon and cannonball before the firing must be equal to the momentum of the cannon and the cannonball after the firing.

Thus,  the cannon has more mass than the ball, which means that it has a greater inertia and will be more resistant to acceleration. This results in a smaller speed of recoil compared to the cannonball.

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(a) The initial velocity of the projectile is 42.23 m/s.

(b) The maximum height reached by the projectile is 91 m.

The initial velocity of the projectile is calculated by applying the following kinematic equation.

v = ( 24.0 î - 8.00j ) m/s

The angle of projection is calculated as;

θ = arc tan ( Vy / Vx )

θ = arc tan ( 8 / 24 )

θ = 18.43⁰

h = ( u² sin²θ ) / 2g

u² = 2gh / (sin²θ)

u² = ( 2 x 9.8 x 9.1 ) / ( sin 18.43 )²

u² = 1783.6

u = √1783.6

u = 42.23 m/s

The maximum height reached by the projectile is calculated as follows;

v² = u² - 2gh

where;

2gh = u²

h = ( u² ) / ( 2g)

h = ( 42.23² ) / ( 2 x 9.8 )

h = 91 m

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The motion that could be represented by the given position-versus-time graph is "A car drives toward the right at first slowly, then faster."

We can see that the graph has a positive slope, which indicates a motion in the positive direction. The fact that the slope is increasing over time means that the object is accelerating, which is consistent with the car starting off slowly and then getting faster.

phase 1 : object moves towards its mean position, velocity must be slow.

phase 2 : object moved to its initial position taking much less time compared to phase 1 but in the same direction to reach its mean position.

Therefore, the correct option is "A car drives toward the right at first slowly, then faster."

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