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Applications of Horizontal and Vertical Components

A ball falls ...

Question

A ball falls from a height of $5$ m and strikes the roof of a lift. If at the time of the collision, lift is moving in the upward direction with a velocity of $1$ m/s, then the velocity with which the ball rebounds after the collision will be $(e = 1)$ :

11

m/s

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12

m/s

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13

m/s

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10

m/s

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Solution

The correct option is D $12$ m/s
$L i f t = m_{2}$ and $B a l l = m_{1}$

$v_{1} = \frac{(m_{2} - m_{1}) u_{1}}{(m_{2} + m_{1})} + \frac{2 m_{2} u_{2}}{m_{1} + m_{2}}$

But $m_{2} >> m_{1},$

$v_{1} = \frac{m_{2} u_{1}}{m_{2}} + \frac{{2 m}_{2} u_{2}}{m_{2}}$

$v_{1} = u_{1} + 2 u_{2}$

Given $h = 5 m$

$v^{2} - u^{2} = 2 g s$

$0 - u^{2} = 2 \times 10 \times 5$

$u_{1} = 10 \frac{m}{s}$ and $u_{2} = 1 \frac{m}{s}$

$v_{1} = 10 + 2 \times 1 = 12 \frac{m}{s}$

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