Question

1. in a game of billiards, you hit the 0.7 kg cue ball at a velocity of 32 m/s. all of the other pool balls it hits fly away at 4 m/s. what was the total mass of all of the pool balls that you broke up?

Explanation:

Step1: <Apply conservation of momentum>

According to the law of conservation of momentum \(m_1v_1 = m_2v_2\), where \(m_1 = 0.7\space kg\), \(v_1=32\space m/s\), \(v_2 = 4\space m/s\).

Step2: <Solve for \(m_2\)>

We can rewrite the formula as \(m_2=\frac{m_1v_1}{v_2}\). Substitute the values: \(m_2=\frac{0.7\times32}{4}\).
First calculate \(0.7\times32 = 22.4\), then \(\frac{22.4}{4}=5.6\space kg\).

Answer:

\(5.6\space kg\)