Question

A 0.01 kg bullet is fired at a 0.5 kg block initially at rest. The bullet, moving with an initial speed of 400 m/s, emerges from the block with a speed of 300 m/s. What is the speed of the block after the collision?

Answer 1

Use the law of conservation of momentum to solve this problem. We have a system of two bodies (bullet and block). Initially, only the bullet has a non-zero momentum. After the collision, both have some momentum and we know the part for the bullet, so it is simple to isolate the part for the block. Call v_t0 the initial bullet speed, v_t1 new bullet speed, v_k speed of block. (similarly for masses):

$m_t\cdot v_{t0}=m_t\cdot v_{t1} + m_k\cdot v_k\implies\\v_k=\frac{m_t\cdot v_{t0}-m_t\cdot v_{t1}}{m_k}=\frac{0.01kg\cdot(400-300)m/s}{0.5kg}=2\frac{m}{s}$

The block will move with a speed of 2 m/s in the direction of the bullet.