A ball is thrown downward from the top of a 120​-foot building with an initial velocity of 13 feet per second. The height of the ball h after t seconds is given by the equation h= -16t^2 - 13t 120

Question

A ball is thrown downward from the top of a 120​-foot building with an initial velocity of 13 feet per second. The height of the ball h after t seconds is given by the equation h= -16t^2 - 13t 120

Answer 1

Maybe the problem is when does it hit the ground? IF so, then' set h=0 and solve for t

-16t^2 -13t + 120 = 0

16t^2 + 13t - 120 = 0

t = -13/32 + or - (1/32)sqr(13^2 + 4(16)(120)) = -13/32 + or - (1/32)(88.6) = about 2.36 seconds

velocity when it hits the ground is calculated from the derivative

h'(2.36) = -32(2.36) -13 = 75.6 - 13 = 62.6 ft./sec