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 $100$ newton so that it attains a vertical height of $ 20 \,m$. The time for which the ball remains in contact with the bat is ........... $\sec$. $[g = 10\,m/{s^2}]$
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 $100$ newton so that it attains a vertical height of $ 20 \,m$. The time for which the ball remains in contact with the bat is ........... $\sec$. $[g = 10\,m/{s^2}]$
$0.12$
$0.08$
$0.04$
$12$
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 $100$ newton so that it attains a vertical height of $ 20 \,m$. The time for which the ball remains in contact with the bat is ........... $\sec$. $[g = 10\,m/{s^2}]$
Velocity by which the ball hits the bat
${v_1} = \sqrt {2g{h_1}} = \sqrt {2 \times 10 \times 5} $ or $\overrightarrow {{v_1}} = + 10\,m/s = 10\,m/s$
velocity of rebound
${v_2} = \sqrt {2g{h_2}} = \sqrt {2 \times 10 \times 20} = 20\,m/s$ or $\overrightarrow {{v_2}} = - 20\,m/s$
$F = m\frac{{dv}}{{dt}} = \frac{{m(\overrightarrow {{v_2}} - \overrightarrow {{v_1}} )}}{{dt}} = \frac{{0.4( - 20 - 10)}}{{dt}} = 100\,N$
by solving $dt = 0.12\,\sec $
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