A 15 g bullet traveling horizontally strikes a 700-g target sitting at the edge

Question

A 15 g bullet traveling horizontally strikes a 700-g target sitting at the edge of a table. The bullet is lodged into the wood. The table height is 2.0 m, and the speed of the bullet was 300 m/s just before it hit the target. How far from the edge of the table does the target hit the floor? What is the initial momentum of the bullet-target system (before the bullet hits the target)? Assuming the impulse from external forces is negligible during the bullet's impact, what is the final momentum of the bullet-target system (immediately after the bullet is embedded)? What is the mass of the target with the bullet stuck in it? What is the horizontal component of velocity of the target and bullet after the bullet is embedded? What is the vertical component of velocity of the target and bullet immediately after the bullet is embedded? With this initial vertical velocity, how much time will it take for the target to fall down to the ground? How far does the target move in the horizontal direction within this time?

Explanation / Answer

Momentum of an object = mv
1) Momentum of bullet before hitting target = 0.015*300 = 4.5 Kg m/sec
   Momentum of target = 0.7*0 = 0
   Momentum of Bullet- target system = sum of momentums = 4.5 Kg m/sec

2) As there is no impuse from external forces, there is no change in momentum of Bullet target system, immediately after the impact.

3) Mass of target with bullet in it = 700 + 15 = 715 gm

4) Using Momentum = mv
velocity of Bullet+target mass = momentum / mass = 4.5 / 0.715 = 6.3 m/s

5) Initial momentum of Bullet or momentum of Bullet+target after impact is along horizotal direction, as bullet was moving in horizontal direction. Hence vertical component of velocity of Bullet+target after the impact is zero.

6) with inital velocity in vertical direction = 0, acceleration g and verticla dispalce of 2m, using
s = ut + 1/2 a t2 we get
2 = 1/2 (9.8) t2
t = 0.64 sec

7) during the fall, velocity in horizontal diection remains constant. Hence displacement in horizontal direction
= vt
= 6.3*0.64 = 4 m

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