Answer: 11369.46 m/s
Explanation:
We have the following data:
[tex]m_{1}=5.8 kg[/tex] is the mass of the bowling ball
[tex]V_{1}=4.34 m/s[/tex] is the velocity of the bowling ball
[tex]m_{2}=2.214 g \frac{1 kg}{1000 g}=0.002214 kg[/tex] is the mass of the ping-pong ball
[tex]V_{2}[/tex] is the velocity of the ping-pong ball
Now, the momentum [tex]p_{1}[/tex] of the bowling ball is:
[tex]p_{1}=m_{1}V_{1}[/tex] (1)
[tex]p_{1}=(5.8 kg)(4.34 m/s)[/tex]
[tex]p_{1}=25.172 kg m/s[/tex] (2)
And the momentum [tex]p_{2}[/tex] of the ping-pong ball is:
[tex]p_{2}=m_{2}V_{2}[/tex] (3)
If the momentum of the bowling ball is equal to the momentum of the ping-pong ball:
[tex]p_{1}=p_{2}[/tex] (4)
[tex]m_{1}V_{1}=m_{2}V_{2}[/tex] (5)
Isolating [tex]V_{2}[/tex]:
[tex]V_{2}=\frac{m_{1}V_{1}}{m_{2}}[/tex] (6)
[tex]V_{2}=\frac{25.172 kg m/s}{0.002214 kg}[/tex] (7)
Finally:
[tex]V_{2}=11369.46 m/s[/tex]
