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JEE Main 2022 (27 Jun, Shift 2) · Terminal Velocity

Terminal Velocity question from JEE Main 2022 (27 Jun, Shift 2)

Q39JEE Main 2022 · 27 JUN · SHIFT 2Medium

Terminal Velocity

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:

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Answer: (b)

Free fall of 4.9 m: $t_1 = \sqrt{\dfrac{2 \times 4.9}{9.8}} = 1$ s, $v = gt_1 = 9.8$ m/s.
Remaining time in water $= 4 - 1 = 3$ s at constant $v$ .
Depth $= 9.8 \times 3 = 29.4$ m
So the answer is (b) 29.4 m.

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