Question

The height of a rocket is h(t) = -4t^2 + 32t, where h(t) is the height in metres t seconds after the rocket is launched. a) How long will the rocket be in the air? b) What is the height of the rocket? c) WHen will the rocket touch the ground?

Answer 1

h(t) = -4t^2 + 32t, this is the eq of parabola whose coefficients are, a=-4, b=32,c=0
when h=0=-4t^2 + 32t solving for t gives...t=8 sec and t=0 the rocket was in the AIR at t=0, the rocket hit the ground at t=8sec
the Velocity V=2ax+b= 2(-4)t+32=-8t+32, its max height reach when
V=0=-8t+32, that is t=32/8=4sec
max h=-4(4)^2 +32=-32meters