A 2.45×10 4 -kg rocket blasts off vertically from the earth\'s surface with a co

Question

A 2.45×104-kg rocket blasts off vertically from the earth's surface with a constant acceleration. During the motion considered in the problem, assume that g remains constant. Inside the rocket, a 14.2-N instrument hangs from a wire that can support a maximum tension of 44.9 N .

Part A

Find the minimum time for this rocket to reach the sound barrier (330m/s) without breaking the inside wire.

Part B

Find the maximum vertical thrust of the rocket engines under these conditions.

Part C

How far is the rocket above the earth's surface when it breaks the sound barrier?

Explanation / Answer

a)

First we need find the acceleration of the rocket

We know that

T -mg =ma====>a =T-mg/m =44.9-14.2/1.45kg=21.17m/s2

The time taken to reach 330m/s is given by

v =u+at

330 =0+(21.17)t

t =15.58s

b)

The maximum vertical thrust is given by

T -mg =ma

T =mg+ma =m(g+a)=2.45*104(9.81+21.17)=76*104N

c)

How far is the rocket above the earth's surface when it breaks the sound barrier is

s =ut+(1/2)at2

s =0+0.5(21.17)(15.58)2 =2569.36m

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