you must determine the acceleration of a rocket so that its equipment can be des

Question

you must determine the acceleration of a rocket so that its equipment can be designed to survive. the rocket will have a burne time of t=30 second, during which time it flies stright up with constant acceleration a cll this phase I of the experiment. after the fuel is exhausted, the rocket will enter free-fall; call this phase II. THE TOTAL TIME OF FIGHT OF THE ROCKET MUST BE t=300 seconds

a) what should you make the acceleration of the rocket,a ,when the engine is on?

b) what is maximum altitude of the rocket?

Explanation / Answer

(a)

Let acceleration = a

Speed achieved in 30 s = 30*a

Distance covered = 1/2*a*(30)^2

Now the Time left is 270 sec which should be taken in covering the remaining distance

APPLY EQUATION OF MOTION FOR REMAINING TIME SPAN

s = u*t + 1/2*(acc.)*t^2

-1/2*a*(30)^2 = (30a)*270 + 1/2*(-9.8)*(270)^2

a = 41.78 m/s^2

(b)

Maximum altitude is when speed is zero

v = u + a*t

0 = 30*a + (-9.8)*t

t = 30a/9.8 = 127.9 s

s = u*t + 1/2*acc*t^2

s1 = (30a)*127.9 + 1/2(-9.8)*(127.9)^2 = 80153.7 m

s2 = 0*(30) + 1/2*(a)*(30)^2 = 18801 m

s1 + s2 = 98955 m

SO ALTITUDE IS 98955 m

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