# Collisions/Projectile Motion (AP Free-response)

• TheFireFox
In summary, the problem involves a bullet of mass m hitting a block of mass 100m on a frictionless table at a height h above the floor. After impact, the bullet and block slide off the table and hit the floor at a distance x from the edge of the table. The speed of the block as it leaves the table can be found using conservation of momentum, and the delta KE (change in kinetic energy) of the system can be calculated using the final and initial kinetic energies. For part C, the horizontal distance x can be found using the final horizontal velocity and the time it takes for the block to hit the floor, which can be found using the distance h and the acceleration due to gravity. Parts D and E involve
TheFireFox

## Homework Statement

3. A bullet of mass m is moving horizontally with speed vowhen it hits a block with mass 100m that is at rest on a horizontal frictionless table. The surface of the table is height h above the floor. After the impact the bullet and the block slide off the table and hit the floor at a distance x from the edge of the table.

Derive expressions in terms of m, h, Vo, and constants.

A. The speed of the block as it leaves the table
B. Delta KE of the system during impact
C. The horizontal distance X.
If the bullet passes through:
D. Is the time to reach the floor greater, smaller or equal/ Why?
E. Is the distance x smaller, greater equal/ Why?

## Homework Equations

I'm assuming that conservation of momentum has something to do with part A; Delta KE= KEf- KEri, and KE= (0.5)mv2 for part B, General kinematics equations for Part C (I'm guessing D= Vit+0.5at2) , and I'm confused about D and E.

## The Attempt at a Solution

A. mVo=(m+100m)Vf
Vf=(mVo) / (m+100m) = mVo / m(1+100) = Vo/101

B. Delta KE = KEf-KEi

=0.5(1+100m)Vf2 - 0.5 mVo2

C. x=Vi + 0.5at2

I'd greatly appreciate any help/feedback.

Your approaches to parts A and B are correct. Part C is not correct because there is no accelerating force in the horizontal, x, direction. So x = Vft. The time, t, is found from h = 1/2gt2 since Vo = 0 (no initial velocity in the vertical or y direction). As for parts D and E, consider if the amount of time for the block to hit the floor is independent or dependent on the initial horizontal velocity, and consider the amount of energy delivered to the block by the bullet if the bullet passed through compared to the bullet remaining in the block and how this would affect the horizontal initial velocity of the block.

Your approach to parts A and B seem correct. However, for part C, you will need to use the equations of motion for projectile motion, since the bullet and the block will have a parabolic trajectory after leaving the table. The equation you provided, x=Vi + 0.5at2, only applies to objects moving with constant acceleration.

For part D, you can use the equation of motion for vertical motion, y= Viy*t + 0.5gt2, where Viy is the initial vertical velocity and g is the acceleration due to gravity. Since the bullet and the block have the same initial vertical velocity, the time to reach the floor will be the same for both objects. This means that the time will be equal whether the bullet passes through the block or not.

For part E, the distance x will be greater if the bullet passes through the block. This is because the bullet will have a greater velocity after passing through the block, which will result in a longer horizontal distance traveled before hitting the floor.

Overall, your understanding of conservation of momentum and kinetic energy is correct, but make sure to use the appropriate equations for projectile motion in part C. Good job!

## What is a collision?

A collision is an event where two or more objects come into contact with each other and exchange energy and/or momentum.

## What is projectile motion?

Projectile motion is the motion of an object that is launched or thrown into the air and moves along a curved path due to the influence of gravity.

## What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a system remains constant in the absence of external forces. This means that in a closed system, the total momentum before a collision is equal to the total momentum after the collision.

## How do you calculate the velocity of an object after a collision?

To calculate the velocity of an object after a collision, you can use the equation: v = (m1v1 + m2v2) / (m1 + m2), where v is the final velocity, m is the mass, and the subscripts 1 and 2 represent the two objects involved in the collision.

## How do you determine the range of a projectile?

The range of a projectile can be determined using the equation: R = v0^2 * sin(2θ) / g, where R is the range, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

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