Collisions/Projectile Motion (AP Free-response)

[TheFireFox]

Homework Statement

3. A bullet of mass m is moving horizontally with speed v_owhen 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, V_o, 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= KE_f- KEr_i, and KE= (0.5)mv² for part B, General kinematics equations for Part C (I'm guessing D= V_it+0.5at²) , and I'm confused about D and E.

The Attempt at a Solution

A. mV_o=(m+100m)V_f
V_f=(mV_o) / (m+100m) = mV_o / m(1+100) = V_o/101

B. Delta KE = KE_f-KE_i

=0.5(1+100m)V_f² - 0.5 mV_o²

C. x=V_i + 0.5at²


I'd greatly appreciate any help/feedback.

 

[chrisk]

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 = V_ft. The time, t, is found from h = 1/2gt² since V_o = 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.

 

[thomate1]

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!