After t seconds, a model rocket launched in the air from ground level reaches a height h feet, where h = -16t2​ + 32t + 48. The rocket then falls back to the ground.

Question

A. After how many seconds will the rocket have reached its maximum height? 

B. What is the maximum height of the rocket?    

C. ​What is the height of the rocket after 2 seconds?       

D.​ After how many seconds after it is launched will the rocket hit the ground?      

    

Answer 1

To get the maximum height, we need to look for the vertex.

x = -b/2a

x = -32/2(-16) = 1 second

h(1) = -16(1)² + 32(1) + 48 = -16 + 32 + 48 = 64 feet

After 1 second, the rocket will reach at the height of 64 feet.

h(2) = -16(2)² + 32(2) + 48 = -64 + 64 + 48 = 48 feet

-16t² + 32t+ 48 = 0

-16(t² - 2t - 3) = 0

-16(t - 3)(t + 1) = 0

t - 3 = 0 or t + 1 = 0

t = 3 or t = -1

The rocket will hit the ground at 3 seconds after the launch.