Question

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
• C. 39.2 m
• D. 73.5 m

Answer 1

Answer: (B)

29.4 m

Answer 2

The approximate depth of the lake is :

$t_1=\sqrt{\frac{2h}{g}} =\sqrt{\frac{2×4.9}{9.8}}=1 s$

$Δt = 4 – 1 = 3 s,$

$v=\sqrt{2gℎ}=\sqrt{2×9.8×4.9}=9.8m/s$

$∴ Depth = 9.8 × 3 = 29.4 m$