Equation h=80t-16t^2 models the height h feet reached in t seconds by an object propelled straight up from the ground.Will the object ever reach a height of 90 ft?

Question

What time would it be reached?

Answer 1

90 = -16t² + 80t

90 = -16(t² - 5t)

90 = -16(t² - 5t + (-2.5)²) + 100

-10 = -16(t - 2.5)²

0.625 = (t - 2.5)²

±√0.625 = t - 2.5

2.5 ± √0.625 = t

Answer 2

Yes, at t = 5/2 the ht will be 100 ft.(Set the derivative= 0)±

At t=(10±√10)/4 seconds (Solve the quadratic) It reaches 90 ft going up and coming down!