Question

A rocket is launched with a constant thrust corresponding to an acceleration of

f (a, t ) =

a ft/sec 2

1
( a − 32)t 2
2

. Neglecting the air resistance, it’s height after t second is given by

feet. Fuel used by the rocket is proportional to

follows the equation
. Find the acceleration so that the rocket will reach
maximum height when the fuel runs out. What is this height?

a 2t

and the limited fuel capacity of the rocket

a t = 10,000

2