Question

A sounding rocket, launched vertically upward with an initial speed of
79.0 m/s,
accelerates away from the launch pad at
5.70 m/s2.
The rocket exhausts its fuel, and its engine shuts down at an altitude of
1.15 km,
after which it moves freely under the influence of gravity.
a) How long is the rocket in the air?
s
b) What is the maximum altitude reached by the rocket?
km
(c) What is the velocity of the rocket just before it strikes the ground?

Answer 1

find the time it takes to get to 1.15km
1.15= +vi*t+5.7/2 t^2
use the quadratic equation to find t.
then find the time to free fly
hf=0=1.15+vb*t-1/2 g t^2
where vb= 79+5.7t under power.
now solve for t in the free fall.
add the two times.