20. A rocket is launched straicht up. The oxpelling gases from the bottom of the
ID: 3308929 • Letter: 2
Question
20. A rocket is launched straicht up. The oxpelling gases from the bottom of the rocket provide it with hcoast ant upward acceleration for 20.0 s/at which point the rocket depletes its fuel supply. The rocket's altitude 25.0 s Constont a from too tot-20s after launch is 6.50 km. Ignore the effects of air resistance. (a) Determine the rocket's initial upward acceleration (b) Determine the rocket's speed at the altitude of 6.50 km. (e) Determine the maximum height to which the rocket reaches and the total time (from launch) that it takes (d) Determine the total flight time of the rocket. to reach this height.Explanation / Answer
20. from 0 to 20s,
yf - yi = v0 t + a t^2 / 2
y1 - 0 = 0 + a(20^2)/2
y1 = 200a
after that rocket will in free fall,
v = v0 + a t = 20 a
after 5 sec,
y2 - y1 = (20 a)(5) + (9.8 x 5^2 / 2)
6500 - 200a = 100 a - 122.625
a = 22 m/s^2 ......Ans
(B) v =20a - (9.8 x5) = (20x 22)- (9.8 x5)
v = 392 m/s
(c) after that vf^2 - vi^2 = 2 a d
0^2 - 392^2 = 2(-9.8)(y3)
y3 = 7858 m
Hmax = y3 + y2 = 14.4 x 10^3 m Or 14.4 km .....Ans
for time,
v = vi + a t
0 = 392 - 9.8 t1
t1 =40 s
t = 40 + 25 = 65 sec .....Ans
(D) after that , yf - yi = v0 t + a t^2 / 2
0 - 14.4x10^3 = 0 - 9.8 t2^2 / 2
t2 = 54.2 sec
t = 65 + 54.2 = 119.2 sec .....Ans
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