posted by Matt on .
Homer Hickham and his buddies launched model rockets in the late 1950's when the US was trying to get a rocket into space. If homer launches a rocket from rest and its engine delivers a constance acceleration of 8.2 m/s^2 for 5.0seconds after which the fuel is used up by the rocket.
A) Find the maximum altitude reached by the rocket.
B) Find the total time the rocket is in flight (up and down)
v = 8.2t
v(5) = 41 m/s
h = 1/2 (8.2) t^2
h(5) = 102.5 m
So, after 5 seconds, the rocket is 102.5 meters up, with a speed of 41.0 m/s.
Now, only gravity provides acceleration, so
h = 102.5 + 41.0t - 4.9 t^2
h=0 when t = 10.382
max h when t = -41.0/-9.8 = 4.18
h(4.18) = 188.265
So, the rocket reaches a max height of 188.27m after 4.18 seconds of ballistic flight, and hits the ground again after 5.0+10.382 = 15.382 seconds have elapsed.