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  4. A ball of mass 400 gm is dropped from a height of 5 m A boy on the ground hits the ball vertically upwards with a bat with an average force of 100 N so that it attains a vertical height of 20 m. The time for which the ball remains in contact with the bat is [g =10 m/s2]

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Q. A ball of mass $400 \,gm$ is dropped from a height of $5 \,m$ A boy on the ground hits the ball vertically upwards with a bat with an average force of $100 \,N$ so that it attains a vertical height of $20 \,m$. The time for which the ball remains in contact with the bat is$ [g =10 \,m/s^{2}]$

Laws of Motion

Solution:

Velocity by which the ball hits the bat
$v_{1}=\sqrt{2gh_{1}}$
$=\sqrt{2\times10\times5}$ or $\vec{v}_{1}= + 10\, m /s=10\, m /s$
Velocity of rebound
$v_{2}=\sqrt{2gh_{2}}$
$=\sqrt{2\times10\times20}=20\, m/ s$ or $\vec{v}_{2}=-20\, m/ s$
$F=m \frac{dv}{dt}=\frac{m\left(\vec{v}_{2}-\vec{v}_{1}\right)}{dt}$
$=\frac{0.4\left(-20-10\right)}{dt}=100\,N$
by solving, $dt =0.12\,sec$