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At the county fair, Chris throws a 0.12kg baseball at a 2.4kg wooden milk bottle, hoping to knock it off its stand and win a prize. The ball bounces straight back at 30% of its incoming speed, knocking the bottle straight forward.What is the bottle's speed, as a percentage of the ball's incoming speed?Express your answer using two significant figures.

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boffeemadrid

Answer:

[tex]6.5\%\ of\ u_1[/tex]

Explanation:

[tex]m_{1}[/tex] = Mass of ball = 0.12 kg

tex]m_{2}[/tex] = Mass of bottle = 2.4 kg

[tex]u_{1}[/tex] = Initial velocity of ball

[tex]u_{2}[/tex] = Initial velocity of bottle

[tex]v_{1}[/tex] = Final velocity of ball = [tex]-0.3u_{1}[/tex]

[tex]v_{2}[/tex] = Final velocity of bottle

As linear momentum is conserved

[tex]m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}\\\Rightarrow 0.12u_{1}+2.4\times 0=-0.12(0.3u_{1})+2.4v_{2}\\\Rightarrow 0.156u_1=2.4v_2\\\Rightarrow \frac{v_2}{u_1}=0.065\\\Rightarrow v_2=0.065\times 100\times u_1\\\Rightarrow v_2=6.5\%\ of\ u_1[/tex]

The bottle's speed is [tex]6.5\%\ of\ u_1[/tex]

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