Question

A 7500kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.25m/s^2 and feels no appreciable air resistance. When it has reached 525m, its engine fails; the only force acting on it now is gravity. (a) What is the maximum height this rocket will reach above the launchpad? (b) How much time will elapse after engine failure before the rocket come crashing down to the launch pad, and how fast will it be moving just before it crashes? (c) sketch ay-t, Uy-t and y-t graphs of the rocket's motion from the instant of blast-off to the instant just before it strikes the launch pad.

Answer 1

Acceleration, $a=2.25\space m/s^2$

Mass, $m=7500\space kg$

Height, $h_1=525\space m$

(a) Velocity of the rocket when engines fail:

$v_1^2=u^2+2as$

Initial velocity, $u=0$

$v_1=\sqrt{2ah_1}=48.61\space m/s$

At maximum height the final velocity goes to zero

$v_2^2=v_1^2-2gh_2$

$h_2=120.56\space m$

Maximum height attained, $h=h_1+h_2=645.56\space m$

(b) $-525=v_1t-\dfrac{1}{2}gt^2$

$4.9t^2-48.6t-525=0$

$\therefore t=16.44\space s$

Let the velocity with which the rocket hits the launchpad = $v_y$

$v_y^2=v_1^2-2\times g\times h_1$

$v_y=-112.5\space m/s$

(c)