Calculate how high the rocket will go before it begins to fall.

Question

A rocket is launched straight up into the sky. When it runs out of fuel it is 425 ft above the ground and traveling at a velocity of 75 feet per second. At that instant it begins to act as an object in free fall. Calculate how high the rocket will go before it begins to fall.

Answer 1

h=-16t^2+75t

h' = -32t + 75 = 0

t = 75/32 = about 2.34375 seconds

max height = h(75/32)

= -16(75/32)^ + 75(75/32) +425

= 5625/64 +425

= about 87.89 + 425 feet

= about 512.89 feet

Answer 2

y = 425 + 75t - 16t²; y' = 75 - 32t = 0; t = 75/32 = 2.342 s

Max height y(7.65) = 425 + 75·2.342 - 16·2.342 = 512.9 ft