A rocket rises vertically, from rest, with an acceleration of 3.2 m/s2 until it

Question

A rocket rises vertically, from rest, with an acceleration of 3.2 m/s2 until it runs out of fuel at an altitude of 715 m . After this point, its acceleration is that of gravity, downward.

Part A

What is the velocity of the rocket when it runs out of fuel?

Express your answer to two significant figures and include the appropriate units.

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Part B

How long does it take to reach this point?

Express your answer to two significant figures and include the appropriate units.

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Part C

What maximum altitude does the rocket reach?

Express your answer to two significant figures and include the appropriate units.

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Part D

How much time (total) does it take to reach maximum altitude?

Express your answer to two significant figures and include the appropriate units.

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Part E

With what velocity does it strike the Earth?

Express your answer to two significant figures and include the appropriate units.

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Part F

How long (total) is it in the air?

Express your answer to two significant figures and include the appropriate units.

A rocket rises vertically, from rest, with an acceleration of 3.2 m/s2 until it runs out of fuel at an altitude of 715 m . After this point, its acceleration is that of gravity, downward.

Part A

What is the velocity of the rocket when it runs out of fuel?

Express your answer to two significant figures and include the appropriate units.

v715m =

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Part B

How long does it take to reach this point?

Express your answer to two significant figures and include the appropriate units.

t715m =

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Part C

What maximum altitude does the rocket reach?

Express your answer to two significant figures and include the appropriate units.

ymax =

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Part D

How much time (total) does it take to reach maximum altitude?

Express your answer to two significant figures and include the appropriate units.

t =

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Part E

With what velocity does it strike the Earth?

Express your answer to two significant figures and include the appropriate units.

v =

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Part F

How long (total) is it in the air?

Express your answer to two significant figures and include the appropriate units.

ttotal =

Explanation / Answer

A)

intial velocity is u = 0 m/s

a = 3.2 m/s^2

distanmce travelled is s = 715 m

v = sqrt(2*a*h) = sqrt(2*3.2*715)= 67.64 m/s

B) time taken is t = sqrt(2*h/a) = sqrt(2*715/3.2) = 21.13 s

C) maximum altitude is 715+S1

S1 = u^2/(2*g) = 67.64*67.64/(2*9.81) = 233.2

then maximum altitude is 715+233.2 = 948.2 m

D) total time taken is 21.13+t1

t1 = u/g = 67.64/9.81 = 6.9 s

then total time taken is 21.13+6.9 = 28.03 s

E) V = sqrt(2*g*Hmax) = sqrt(2*9.81*948.2) = 136.4 m/s

F) Total time in air is T = 28.03+sqrt(2*Hmax/g) = 28.03+sqrt(2*948.2/9.81) = 28.03+13.9 = 41.93 s

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