You have a summer job working for a University research group investigating the

Question

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

.Known:

Unknown:

Strategy:

Solution:

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 + a*t
V = a*30

Distance reached by Rocket in 30.0s -
S = u*t + 1/2*a*t^2
S = 0 + 1/2 * a * 30^2
S = 1/2 * a * 30^2
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/s^2 downwards

Using Newton equation of motion -
S = ut + 1/2 * at^2
Taking Downward direction to be positive.

450 a = - 30a * 270 + 1/2 * 9.8 * 270^2
Solving for a
a = 41.8 m/s^2

Acceleration of the rocket for sucessfull mission, a = 41.8 m/s^2

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