A 7.50-kg bowling ball strikes a 5.20-kg pin.The pin flies forward with a velocity of 4.00 m/s;the ball continues forward at 5.50 m/s.What was the original velocity of the ball?

Question

Quizplus · Accepted Answer

We can use conservation of momentum to solve this problem.
Let's consider the x-direction as the direction of motion.
The initial momentum of the system (bowling ball + pin) is:
P_initial = m_bowling_ball * v_initial_ball
The final momentum of the system is:
P_final = m_bowling_ball * v_final_ball + m_pin * v_pin
where v_final_ball = 5.50 m/s (given) and v_pin = 4.00 m/s (given).
Using conservation of momentum, we have:
P_initial = P_final
m_bowling_ball * v_initial_ball = m_bowling_ball * v_final_ball + m_pin * v_pin
Solving for v_initial_ball, we get:
v_initial_ball = (m_bowling_ball * v_final_ball + m_pin * v_pin)/m_bowling_ball
Substituting the values given, we get:
v_initial_ball = (7.50 kg * 5.50 m/s + 5.20 kg * 4.00 m/s)/7.50 kg
v_initial_ball = 8.27 m/s
Therefore, the original velocity of the ball was 8.27 m/s, which corresponds to choice B.

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