A miniature spring-loaded,radio-controlled gun is mounted on an air puck.The gun's bullet has a mass of 5.00 g,and the gun and puck have a combined mass of 130g.With the system initially at rest,the radio controlled trigger releases the bullet causing the puck and empty gun to move with a speed of 0.500 m/s.What is the bullet's speed?
A) 4.80 m/s
B) 13.0 m/s
C) 48.0 m/s
D) 12.5 m/s

Question

Quizplus · Accepted Answer

We can use the conservation of momentum to solve this problem. Initially, the momentum of the system is zero because it is at rest. After the gun is fired, the momentum of the system is:

(m_bullet)(v_bullet) + (m_system)(v_system) = 0

where v_bullet is the speed of the bullet, and v_system is the speed of the puck and empty gun. We can solve for v_bullet:

v_bullet = -(m_system/m_bullet) v_system 
       = -(130 g / 5.00 g) (0.500 m/s)
       = -13.0 m/s

The negative sign indicates that the bullet is moving in the opposite direction of the puck and gun. Taking the absolute value gives:

|v_bullet| = 13.0 m/s

Therefore, the bullet's speed is 13.0 m/s, which corresponds to choice B.

A Miniature Spring-Loaded,radio-Controlled Gun Is Mounted on an Air Puck