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?
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.