Question

A rocket follows a parabolic trajectory. After t seconds, the vertical height above the ground, in metres, is given by H=37t - t (squared).

What is the maximum height of the rocket after 10 seconds?

What is the max height of the rocket?

What time does it reach the maximum height?

How long is the rocket in the air for?

Answer 1

h = 37 t - t^2
at t = 10
h = 370 - 100 = 270

dh/dt = 0 at top = 37 - 2t
t = 37/2 = 18.5 seconds to top
h = 37(18.5) -18.5^2 = 342

when is h = 0 again?
t(t-37) = 0
t = 37 seconds
(which of course is 18.5 times two)

Answer 2

this doesnt make any sense wtd is dh