A 20.0-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.If the block had been originally at rest and is free to move,what is its resulting speed?
A)22.0 m/s
B)18.0 m/s
C)20.0 m/s
D)2.00 m/s
E)45.0 m/s

Question

Quizplus · Accepted Answer

According to conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Let the velocity of the block after the collision be V.
Initial momentum = m1v1 + m2v2 (where m1 and v1 are the mass and velocity of the bullet and m2 and v2 are the mass and velocity of the block)
= 0.02 kg * 1000 m/s + 1 kg * 0 m/s
= 20 kg m/s
Final momentum = (m1 + m2)V
= 0.02 kg * 100 m/s + 1 kg * V
= (1.02 kg)V
Since initial momentum = final momentum:
20 kg m/s = (1.02 kg)V
V = 19.6 m/s (rounded to one decimal place)
Therefore, the resulting speed of the block is 19.6 m/s. The closest answer choice is B, which is 18.0 m/s. This could be due to rounding or approximations made in the calculation.

A 200-G Bullet Moving at 1 000 M/s Is Fired Through