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 120 g.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)11.5 m/s
C)48.0 m/s
D)12.0 m/s

Question

Quizplus · Accepted Answer

We can use the conservation of momentum to solve this problem. Since there are no external forces acting on the system, the total momentum of the system must be conserved.

Initial momentum = Final momentum

Since the system is initially at rest, the initial momentum is zero.

Final momentum = (m_puck + m_gun + m_bullet) * v_final

where m_puck = mass of the puck, m_gun = mass of the gun, m_bullet = mass of the bullet, and v_final = final velocity of the puck and gun.

Plugging in the given values, we get:

0 = (0.120 kg + 0.005 kg) * 0.500 m/s + m_bullet * v_bullet

Solving for v_bullet, we get:

v_bullet = -[(0.120 kg + 0.005 kg) * 0.500 m/s]/0.005 kg

v_bullet = -12.0 m/s (Note that the negative sign indicates that the bullet is moving in the opposite direction of the puck and gun)

Taking the absolute value, we get:

v_bullet = 12.0 m/s

Therefore, the bullet's speed is 12.0 m/s (Choice D).

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