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A model rocket blasts off and moves upward with an acceleration of 11m/s2 until it reaches a height of 30m , at which point its engine shuts off and it continues its flight in free fall.

A. What is the maximum height attained by the rocket?

B. What is the speed of the rocket just before it hits the ground? (answer in m/s)

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A. Take upward direction as positive.

Initial velocity vo = 0

Let v1 = velocity just before the engine shuts off,

a1 = acceleration before the engine shuts off,

h1 = height moved with acceleration a1 = 30 m,

v2 = velocity at maximum height = 0,

h2 = height covered after the engine shuts off

v1^2 = vo^2 + 2*a*h1

v1^2 = 0 + 2 * 11 * 30 = 660

v2^2 = v1^2 - 2g*h2

0 = 660 - 2 * 9.8 * h2

h2 = 660/19.6 = 33.67 m

h1 + h2 = 30 + 33.67 = 63.67 m

B. Let the speed = v3

v3 = sqrt(2g(h1+h2)) = sqrt(2 * 9.8 * 63.67) = 35.33 m/s

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