A ball thrown upward height above the ground after t seconds is H ( t ) = 88 ⋅ t − 16 t ^2 feet. Find the time t when the ball will be traveling downward at 22 feet per second

Question

A ball thrown upward in the air, and its height above the ground after t seconds is H ( t ) = 88 ⋅ t − 16 t ^2 feet. Find the time t when the ball will be traveling downward at 22 feet per second

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

Answer 1

There is a typo, the equation should be:

H(t) = 88⋅t − 16⋅t^2

t is the time in seconds

H(t) is the height in feet as a function of time

88ft/s is the velocity at t=0

16 = 1/2*(32ft/s^2) where 32ft/s^2 is the acceleration due to gravity at Earth's surface

The velocity as a function of time is the 1st derivative of the height with respect to time:

d/dt(H(t)) = V(t)

To find the the time when the ball's velocity is equal to -22ft/s you need to set your equation for V(t) equal to -22ft/s and solve for t.

Those are the steps. Let me know if you need any clarification or help working through the math.