A model rocket is launched from a raised platform at a speed of 144 feet per second. Its height in feet is given by h (t) = - 16 t 2 + 144 t + 20 (t = seconds after launch). After how many seconds does the object reach its maximum height?

Answer: after 4.5 seconds

Step-by-step explanation:

Given the eqn of the height reached by the rocket.

h (t) = - 16t^2 + 144t + 20

Note: at the maximum height dh (t) / dt = 0

Therefore, differentiating the eqn of height.

dh (t) / dt = - 32t + 144

Equating dh (t) / dt to zero, we have.

-32t+144=0

32t=144

t = 144/32

t = 4.5 seconds