A heavy ball is dropped into a lake from a height of 30.0 m above the water.It hits the water with a certain velocity and continues to sink to the bottom of the lake at this same constant velocity.It reaches the bottom of the lake 10.0 s after it was dropped.How deep is the lake?
A)182.5 m
B)87.4 m
C)29.6 m
D)143.1 m
E)209.7 m

Question

Quizplus · Accepted Answer

The ball first falls 30.0 m under the influence of gravity. The time to fall this distance can be found using the equation $d = \frac{1}{2}gt^2$, where $d$ is the distance, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $t$ is the time in seconds. Solving for $t$, we find the time it takes to fall 30.0 m. Then, knowing it takes a total of 10.0 s to reach the bottom of the lake, we subtract the time it took to fall to the water's surface to find how long it was sinking in the water. Since it sinks at a constant velocity (the same it had upon hitting the water), we can calculate the depth of the lake by adding the distance it fell to the distance it sank, which gives us 182.5 m.

A Heavy Ball Is Dropped into a Lake from a Height