A rocket rises vertically, from rest, with an acceleration of 3.2 m/s^2 until it

Question

A rocket rises vertically, from rest, with an acceleration of 3.2 m/s^2 until it runs out of fuel at an altitude of 820 m. After this point, it’s acceleration is that of gravity, downward. What is the velocity of the rocket when it runs out of fuel? How long does it take to reach this point? What maximum altitude does the rocket reach? How much time total does it take to reach maximum altitude? With what velocity does it strike the earth? How long (total) is it in the air? A rocket rises vertically, from rest, with an acceleration of 3.2 m/s^2 until it runs out of fuel at an altitude of 820 m. After this point, it’s acceleration is that of gravity, downward. What is the velocity of the rocket when it runs out of fuel? How long does it take to reach this point? What maximum altitude does the rocket reach? How much time total does it take to reach maximum altitude? With what velocity does it strike the earth? How long (total) is it in the air? What is the velocity of the rocket when it runs out of fuel? How long does it take to reach this point? What maximum altitude does the rocket reach? How much time total does it take to reach maximum altitude? With what velocity does it strike the earth? How long (total) is it in the air?

Explanation / Answer

given

intial velcoti u = 0

acceleration a = 3.2 m/s^2

given altitude h = 820 m

a) from the relation

v^2-u^2 = 2as

v = sqrt(2*3.2*820) = 72.4 m/s

b) v = u+at

v = at

t = v/a = 72.4/3.2 = 22.625 sec

c) at maximum height velocity is zero

now initial velocity is 72.4 m/s

v^2-u^2 = 2as

here v = 0

u = 72.4 m/s

a = -9.81 m/s^2

h' = 72.4^2/2*9.81 = 267.2 m

total height from ground = 820+267.2 = 1087.2 m

d) t' = 72.4/9.81 = 7.28 sec

total time t = 22.625+7.28 = 29.905 sec

e) v^2 = u^2+2gh

v = sqrt(72.4^2+2*9.81*820) = 146.05 m/s

f) v = u+at

-146.05 = 72.4-9.81*t

t = 22.27 sec

total time is in the air is = 22.27+22.625 = 44.895 sec

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