A 3.00-g bullet traveling horizontally at 400 m/s hits a 3.00-kg wooden block, which is initially at rest on a smooth horizontal table. The bullet buries itself in the block without passing through. The speed of the block after the collision is:
A) 1.33 m/s
B) 0.40 m/s
C) 12.0 m/s
D) 40.0 m/s
E) 160 m/s

Question

Quizplus · Accepted Answer

The conservation of momentum holds true for this collision because we can assume there are no external forces acting on the system. That means the total momentum before the collision (of just the bullet) must equal the total momentum after the collision (of the bullet and block). We can write this as:

(m_bullet)(v_bullet) = (m_bullet + m_block)(v_final)

where:
m_bullet = 3.00 g = 0.00300 kg (mass of bullet)
v_bullet = 400 m/s (initial velocity of bullet)
m_block = 3.00 kg (mass of block)
v_final = final velocity of bullet and block after collision (which is the same for both due to them sticking together)

Simplifying and solving for v_final, we get:

v_final = (m_bullet)(v_bullet) / (m_bullet + m_block)

v_final = (0.00300 kg)(400 m/s) / (0.00300 kg + 3.00 kg)

v_final = 0.3992 m/s ≈ 0.40 m/s

Therefore, the best choice is B, with a final speed of 0.40 m/s.

A 300-G Bullet Traveling Horizontally at 400 M/s Hits a 3