During your summer internship for an aerospace company, you are asked to design

Question

During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 940 m above the earth's surface. The rocket's engines give the rocket an upward acceleration of 16.0 m/s2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance.

What must be the value of T in order for the rocket to reach the required altitude?

Explanation / Answer

Here ,

acceleration of the rocket , a = 16 m/s^2

total height , H = 940 m

let the time taken for rocket to stop after acceleration is t

as 16 * T = 9.8 * t

t = 1.63 * T

Now, for height = 940 m

h = 0.5 * 16 * T^2 + 0.5 * 9.8 * t^2

940 = 0.5 * 16 * T^2 + 0.5 * 9.8 *(1.63 *T)^2

solving for T

T = 6.687 s

the time for which the rocket should accelerate is 6.687 s

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