A ball is thrown upward in the air, and its height above the ground after t seconds is

Question

A ball is thrown upward in the air, and its height above the ground after t seconds is

H(t) = 97⋅t - 16t² feet

Find the time t when the ball will be traveling downward at 48.5 feet per second.

Give your answer as a decimal approximation with at least 3 decimal places.

t = ____ seconds

Answer 1

The ball is traveling downward at 48.5 feet per second means it's velocity v(t) = - 48.5 feet/sec.

v(t) = H'(t) = 97 - 32t

97 - 32t = - 48.5

t = 4.547 seconds

Answer 2

Derive the first derivative of H(x), H'(x)

Calculate H'(t) = 48.5