You have a job working for a University research group investigating ozone deple

Question

You have a job working for a University research group investigating ozone depletion in the atmosphere. The plan is to collect data on the chemical composition of the atmosphere as a function of the distance from the ground using a mass spectrometer located in the nose cone of a rocket fired vertically. To make sure the delicate instruments survive the launch, your task is to determine the acceleration of the rocket before it uses up its fuel. The rocket is launched straight up with a constant acceleration until the fuel is gone 30 seconds later. To collect enough data, the total flight time must be 5.0 minutes before the rocket crashes to the ground.

Explanation / Answer

Let the acceleration of rocket = a
Time taken by rocket to reach back ground = 5.0 min = 300 s

Initial Velocity, u = 0
Acceleration time, t = 30 s

Calculating Velocity attained by Rocket after 30.0 sec -
v = u + at
v = 30a

Distance reached by Rocket in 30.0s -
S = ut + 0.5at2
S = 0 + 0.5a(302)
S = 450 a

Now at this Height,

Initial Velocity = 30a (upwards)
Distance, s = 450 a (downwards)
time, t = 300 - 30 = 270 s
a = 9.8 m/s2 downwards

Using Newton equation of motion -
S = ut + 0.5* at2
Taking Downward direction to be positive.

450 a = {(- 30a) *( 270)} + {(0.5 * 9.8 * 2702)}
Solving for a
a = 41.8 m/s2

Acceleration of the rocket before it uses up its fuel, a = 41.8 m/s2

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