A balloon is rising up with constant velocity of 10 m/s at height of 15 m from the ground. At that instant, a stone of mass 1 kg is dropped from it. Find kinetic energy of stone just before reaching at the ground.

Q: A balloon is rising up with constant velocity of 10 m/s at height of 15 m from the ground. At that instant, a stone of mass 1 kg is dropped from it. Find kinetic energy of stone just before reaching at the ground.

(a) 100 J

(b) 200 J

(c) 300 J

(d) 400 J

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Ans: (b)
Sol:$\displaystyle -15 = 10 t – \frac{1}{2} g t^2$

$\displaystyle 5 t^2 – 10 t -15 = 0 $

$\displaystyle t^2 – 2 t -3 = 0 $

$\displaystyle (t-3)(t+1) = 0 $

t = 3 sec

v = -10 + gt

v = -10 + 10 x 3 = 20 m/s

$\displaystyle K.E = \frac{1}{2} m v^2 $

$\displaystyle K.E = \frac{1}{2} \times 1 \times 20^2 $

K.E = 200 J