Q: A balls dropped into a pond from a diving board 5 m above the water surface. It hits the water surface and moves with constant velocity inside the water. During striking with water surface, 50% velocity of ball is lost. Total time taken by ball to reach at bottom is 10 s after it was dropped. The depth of the pond is

(a) 50 m

(b) 100 m

(c) 90 m

(d) 45 m

Ans: (d)

Sol: Time taken by ball to reach the water surface $t = \sqrt{\frac{2 h}{g}}$

$t = \sqrt{\frac{2 \times 5}{10}} = 1 sec $

Time taken by ball to reach the bottom = 10 -1 = 9 sec

Velocity with which ball hits the water surface $ v = \sqrt{2 g h}$

$ v = \sqrt{2 \times 10 \times 5} = 10 m/s $

Velocity after striking , v = 5 m/s

Depth of pond is , h = 5 × 9 = 45 m