Question

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.

Answer 1

Answer:

$6.5\%\ of\ u_1$

Explanation:

$m_{1}$ = Mass of ball = 0.12 kg

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

$u_{1}$ = Initial velocity of ball

$u_{2}$ = Initial velocity of bottle

$v_{1}$ = Final velocity of ball = $-0.3u_{1}$

$v_{2}$ = Final velocity of bottle

As linear momentum is conserved

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

The bottle's speed is $6.5\%\ of\ u_1$