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Question

A ball is thrown into a lake from a tower 20 m above the water surface. The ball hits the water after 1 sec with a velocity v and then sinks to the bottom of the lake. It comes to rest at the bottom of the lake 6 sec after it was thrown. Find the acceleration of the ball inside the lake and the depth of the lake.

A
5 m/s2, 62.5 m
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B
5 m/s2, 75 m
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C
5 m/s2, 62.5 m
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D
5 m/s2, 75 m
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Solution

The correct option is C 5 m/s2, 62.5 m
Let u be the velocity with which the ball is thrown.
Using 2nd equation of motion, (taking downward +ve)
h=ut+12gt220=u×1+12×10×12u=15 m/s

The velocity of the ball as it is about to touch the surface of the water, v=u+atv=15+10×1v=25 m/s

The ball takes (61)=5 sec to reach from the surface to the bottom of the lake.

For the ball's motion inside water, u=25 m/s, v=0 and t=5 seconds
v=u+at0=25+a×5a=5 m/s2
The negative sign of acceleration shows that the ball slows down while traveling inside the water of the lake.

The depth of the lake, s=ut+12at2s=25×512×5×52s=(12562.5) ms=62.5 m

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