Question

Chapter 02, Problem 62


A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 90.3 m/s2 for 1.75 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?

Answer 1

well, under acceleration, the height h is

h(t) = (1/2)90.3 t^2
At t = 1.75, the height is 138.27 m

Since v = at, at t=1.75, the upward velocity is 158.03 m/s

Now it goes ballistic (really!) and the height is given by

h(t) = 138.27 + 158.03t - 4.9t^2

That's just a parabola. Find its vertex using your favorite method, and that is the maximum height.