A small ball is dropped from a balloon moving vertically up at a speed 10 m/s when the balloon is at a height 15 m from the ground. Neglect air friction and take g = 10m/s². Which of the following is not a suitable to the present situation ?

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The ball covers a distance of 25 m

The ball moves up at a speed 10 m/s at an instant when it is dropped from the balloon

The ball reaches the ground in 3 s

The magnitude of average velocity of the ball is 8.33 m/s.

answer is A.

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Detailed Solution

The maximum height Reached by the ball after through from the balloon
$h = \frac{u^{2}}{2 g} = \frac{100}{2 \times 10} = 5 m$
Distance travelled by the ball = 5+5+15 = 25m
$\begin{array}{l} - h = ut - \frac{1}{2} {gt}^{2} \\ - 15 = 10 t - \frac{1}{2} \times 10 t^{2} \\ 5 t^{2} - 10 t - 15 = 0 \\ t^{2} - 2 t - 3 = 0 \\ t^{2} - 3 t + t - 3 = 0 \\ t (t - 3) + 1 (t - 3) = 0 \\ (t + 1) (t - 3) = 0 \\ t = 3, - 1 \end{array}$