Question

A stone is dropped from the top of a building 122.5 meters above the ground. Suppose the distance the stone travels from its starting point is described by s(t) = 4.9t², where t is in seconds. How fast is the stone traveling when it hits the ground?

Answer 1

Answer:

The speed of stone traveling when it hits the ground = 49 m/s

Explanation:

Height of drop = 122.5 m

Given that distance the stone travels from its starting point

                s(t) = 4.9t²

Substituting height

                122.5 = 4.9t²

                  t² =   25

                  t = 5 seconds

So after 5 seconds stone hit the ground, we need to find velocity when t = 5 seconds.

         Differentiating displacement with respect to time to get velocity,

                   s'(t) = 4.9 x 2 t = 9.8 t

          Velocity when t = 5, s'(5) = 9.8 x 5 = 49 m/s

     The speed of stone traveling when it hits the ground = 49 m/s