A boy jumps from rest, straight down from the top of a cliff. He falls halfway down to the water below in 0.866 s. How much time passes during his entire trip from the top down to the water? Ignore air resistance.

Entire trip takes 1.22 seconds.

Explanation:

We have equation of motion s = ut + 0.5 at²

Initial velocity, u = 0 m/s

Acceleration, a = 9.81 m/s²

Time, t = 0.866 s

Substituting

s = ut + 0.5 at²

s = 0 x 0.866 + 0.5 x 9.81 x 0.866²

s = 3.68 m

Halfway is 3.68 m

Total height = 2 x 3.68 = 7.36 m

We have equation of motion s = ut + 0.5 at²

Initial velocity, u = 0 m/s

Acceleration, a = 9.81 m/s²

Time, t = ?

Displacement, s = 7.36 m

Substituting

s = ut + 0.5 at²

7.36 = 0 x t + 0.5 x 9.81 x t²

t = 1.22 s

Entire trip takes 1.22 seconds.