Math word problem

Question

If an object is propelled upward from a height of 48 feet at an initial velocity of 80 ft./s then its height in feet after T seconds is given by the equation h=-16t^2+80t+48. After how many seconds will the object reach the height of 148 feet?

Answer 1

Set h(t) equal to 148 and solve for t.

148 = -16t^2 + 80t + 48

-16t^2 + 80t - 100 = 0

16t^2 - 80t + 100 = 0

Note this is a perfect square.

(4t - 10)^2 = 0

Solve for t and finish from here. Also note that 148 ft is the maximum possible height.