Question

At t = 0, a stone is dropped from a cliff above a lake; 2.4 seconds later another stone is thrown downward from the same point with an initial speed of 35 m/s. Both stones hit the water at the same instant. Find the height of the cliff in meters.

Answer 1

Let h = height of cliff.

Thus, for the first stone,

-h = -1/2 g t^2

For the second stone,

-h = -35(t - 2.4) - 1/2 g(t-2.4)^2

Subtracting these two equations, and solving for t,

t = 4.8585 s

Thus, solving for h,

h = 116 m [ANSWER]