Question

a cue stick has a mass of 0.5 kg. the cue stick hits a ball with a mass of 0.2 kg at a velocity of 2.5 m/s. what is the velocity of the ball after it is hit? (1 point)

2.5 m/s

6.3 m/s

3.6 m/s

8.3 m/s

Explanation:

Step1: Apply Conservation of Momentum

Assume the cue stick's velocity before collision is \( v_1 = 2.5 \, \text{m/s} \), mass \( m_1 = 0.5 \, \text{kg} \), ball's mass \( m_2 = 0.2 \, \text{kg} \), and ball's initial velocity \( v_2 = 0 \, \text{m/s} \) (at rest). After collision, assume the cue stick stops (simplified, common in such problems), so momentum before equals momentum after: \( m_1v_1 + m_2v_2 = m_2v_2' \).

Step2: Substitute Values

\( (0.5)(2.5) + (0.2)(0) = (0.2)v_2' \)
\( 1.25 = 0.2v_2' \)
\( v_2' = \frac{1.25}{0.2} = 6.25 \approx 6.3 \, \text{m/s} \).

Answer:

B. 6.3 m/s (Note: Using the option label as per the problem's multiple-choice setup, assuming the second option is 6.3 m/s)