A man in a balloon rising vertically with an acceleration of $4.9\,m/{\sec ^2}$ releases a ball $2$ sec after the balloon is let go from the ground. The greatest height above the ground reached by the ball is...........$m$ $(g = 9.8\,m/{\sec ^2})$
A man in a balloon rising vertically with an acceleration of $4.9\,m/{\sec ^2}$ releases a ball $2$ sec after the balloon is let go from the ground. The greatest height above the ground reached by the ball is...........$m$ $(g = 9.8\,m/{\sec ^2})$
$14.7$
$19.6$
$9.8$
$24.5$
A man in a balloon rising vertically with an acceleration of $4.9\,m/{\sec ^2}$ releases a ball $2$ sec after the balloon is let go from the ground. The greatest height above the ground reached by the ball is...........$m$ $(g = 9.8\,m/{\sec ^2})$
Height travelled by ball (with balloon) in $2$ sec
${h_1} = \frac{1}{2}a\;{t^2} = \frac{1}{2} \times 4.9 \times {2^2} = 9.8\;m$
Velocity of the balloon after 2 sec
$v = a\;t = 4.9 \times 2 = 9.8\;m/s$
Now if the ball is released from the balloon then it acquire same velocity in upward direction.
Let it move up to maximum height ${h_2}$
${v^2} = {u^2} - 2g{h_2}$ $⇒$ $0 = {(9.8)^2} - 2 \times (9.8) \times {h_2}$$\therefore $${h_2}=4.9\,m$
Greatest height above the ground reached by the ball $ = {h_1} + {h_2} = 9.8 + 4.9 = 14.7\;m$
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