JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Kinematics

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When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

(A)19.6 m
(B)29.4 m✓ Correct
(C)39.2 m
(D)73.5 m

Answer: (B)

Solution

The ball falls freely from 4.9 m, so using

v^{2} = 2 g h

, we get

v = 2 \times 9.8 \times 4.9 = 9.8

m/s. Time to fall 4.9 m is

t_{1} = \frac{2 h}{g} = 1

s. The ball then sinks with constant velocity 9.8 m/s for the remaining

4.0 - 1.0 = 3.0

s. Depth of lake =

9.8 \times 3 = 29.4

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Single correct option

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