Question

A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground with an initial velocity of 152 feet per second. The height h, in feet, of the rocket above the ground as t seconds after launch is given by the function h(t)=-16t^2+152t+9. How long will it take the rocket to reach its maximum height? What is the maximum height?

Answer 1

Answer:109

Explanation:

h(t) = -16t^2 + 80t + 9.

compare with equation ax%5E2%2Bbx%2Bc=0

a=-16, b=80 c =9

time to go to height h = -b%2F2a

=(80/32)= 2.5 s

time to go maximum height is t = = = = 2.5 seconds.

The maximum height you can get by substituting this value t= 3.5 in the formula

h(t) = -16t^2 + 80t + 9

h(2.5) = -16*2.5^2 + 80*2.5 + 9.

h =109m