Question

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.

Answer 1

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.