A model rocket is launched straight upward with an initial speed of 57.0 m/s. It accelerates with a constant upward acceleration of 1.50 m/s2 until its engines stop at an altitude of 190 m.

Question

(a) What is the maximum height reached by the rocket?
(b) How long after liftoff does the rocket reach its maximum height?
(c) How long is the rocket in the air?

Answer 1

figure the velocity at max altitude

vf^2=vi^2-2ad

now, max height:
You know the KE and PE at 190 meters.

ke+PE at 190 =final PE
so now, figure final height max from the final PE at the top.

now time to max height.
Do it in two parts:
a. time up to shutoff: average velocity you know (vfshut+Vi)/2, and distance. Figure height.
b. the coasting part. You know the initial velocity (vfshut), and the final velocity at the top (zero). average velocity then vfshut/2. You know the distance (height in a - 190m).figure time for this leg
add time for both legs.

Answer 2

I got 192.6 meters as my max height, but I don't think that's right. We haven't learned KE and PE yet.