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 980 m above the earth's surface. The rocket's engines give the rocket an upward acceleration so it moves with the 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?

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Asked Aug 28, 2019
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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 980 m above the earth's surface. The rocket's engines give the rocket an upward acceleration so it moves with the 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? 

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Expert Answer

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Step 1

Given Information :
Rocket is launched from rest .
Initial velocity of the rocket u = 0
Maximum height reached by the rocket H = 980 m
Acceleration of the rocket during the time(T) when it is fired is = 16 m/s2 (upwards)

Step 2

Distance travelled by the rocket during time “T”  ( when it is firing )

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s ut at2 S (0)T(16)T S1 8T2

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Step 3

Distance travelled by the rocket after shutting ...

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After engine shut off acceleration of the rocket will be a -9.81 m/s2 negative sign because motion of rocket is upwards, and acceleration is in downward direction due to gravity) Velocity of the rocket just after engine shut off V uat V = 0 (16)T V 16T Distance travelled by the rocket after engine shutoff Just after engine shut off ,velocityu = 16T At maximum height velocity of the rocket v = 0 v2-u2 2as 1 0 (16T)2 2(-9.81)S2 S2 13.04T2

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