A rocket blasts off vertically from rest on the launch pad with a constant upwar

Question

A rocket blasts off vertically from rest on the launch pad with a constant upward acceleration of 2.20 m/s2 . At 20.0 s after blastoff, the engines suddenly fail, and the rocket begins free fall.

What is the height of the rocket when the engine fails? Express your answer to three significant figures.

Find the magnitudes of the rocket's velocity and acceleration at its highest point. Express your answers, separated by a comma, to two signficant figures.

How long after it was launched will the rocket fall back to the launch pad? Express your answer to three significant figures.

Explanation / Answer

a = 2.2 m/s^2 ; t = 20 s

from eqn of motion:

S = ut + 1/2 at^2

S = 0 + 0.5 x 2.2 x 20^2 = 440 m

So at S = 440 m, the engine fails.

At highest point,

v = 0 and a = g = 9.8 m/s^2

v = at = 2.2 x 20 = 44 m/s

h = v^2/2g = 44^2/2 x 9.8 = 98.78 m

t1 = sqrt(2h/g) = sqrt(2 x 98.78/9.8) = 4.5 s

H = S + h = 440 + 98.78 = 538.78

t2 = sqrt (2H/g) = sqrt (2 x 538.78/9.8) = 10.5 s

total time = 20 + 4.5 + 10.5 = 35 s

Hence, T = 35 s

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