After how many seconds is the height 36 feet?

Question

If an object is propelled upward from a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation h=−16t^+vt+s, where h is in feet. If the object is propelled from a height of 8 feet with an initial velocity of 64 feet per second, its height h is given by the equation h=−16t^2+64t+8. After how many seconds is the height 36 feet?

Answer 1

h(t) = -16t² + 64t + 8

 

Set h = 36 and solve for t.

 

36 = -16t² + 64t + 8

 

-16t² + 64t - 28 = 0

 

Using the quadratic formula,

 

t = 0.5 sec and 3.5 sec

 

It reaches 36 ft in 0.5 sec on the way up and again in 3.5 sec on the way down.