Finding time with an initial velocity of 29ft/s.

Question

A ball is thrown at an initial height of 3 feet with an initial upward velocity at 29 ft/s. The balls height h (in feet) after t seconds is give by: h= 3 + 29t -16t^2. Find the values of t if the balls height is 15ft. Round your answer(s) to the nearest hundredth.

Any help would be greatly appreciated and thanks in advance.

Answer 1

Set h(t)=15 and solve for t.

-16t² + 29t + 3 = 15

-16t² + 29t - 12 = 0

Solve for t using the quadratic formula. You will get two positive solutions for t. The lower solution is the time to reach 15 on the way up. The higher solution is the time to reach 15 on the way down.