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A model rocket is launched straight upward with an initial speed of 44.0 m/s. It accelerates with a constant upward acceleration of 2.50 m/s2 until its engines stop at an altitude of 200 m.a) How long is the rocket in the air?

Question

A model rocket is launched straight upward with an initial speed of 44.0 m/s. It accelerates with a constant upward acceleration of 2.50 m/s2 until its engines stop at an altitude of 200 m.

a) How long is the rocket in the air?

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Step 1

Consider the initial speed of rocket be u, the acceleration of the rocket be a, the speed of the rocket just before the engines stop be v, the displacement of the rocket, that is, the altitude be s, the time interval for the rocket in the air be t, and the displacement of the rocket after the engines stop be h’.

 

Write the equation of motion, and solve for the speed of the rocket just before the engines stop.

,2
= J(4.0 m/s) + 2(2.50 m/s2)(200 m)
= 54.185 m/s
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,2 = J(4.0 m/s) + 2(2.50 m/s2)(200 m) = 54.185 m/s

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Step 2

Write the equation of motion, and solve for the displacement of the rocket after the engines stop.

v2= u2+2gh
(54.185 m/s) (0)2(9.81 m/s2)h"
h' 149.64 m
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v2= u2+2gh (54.185 m/s) (0)2(9.81 m/s2)h" h' 149.64 m

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Step 3

The total height or altitude of the ...

h sh'
(200 m)+(149.64 m)
= 349.64 m
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h sh' (200 m)+(149.64 m) = 349.64 m

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