Laws Of Motion Question 298
Question: A 5000 kg rocket is set for vertical firing. The exhaust speed is$ 800m{{s}^{-1}} $ . To give an initial upward acceleration of$ 20m{{s}^{-2}} $ , the amount of gas ejected per second to supply the needed thrust will be $ ( g=10m{{s}^{-2}} ) $
Options:
A) $ 127.5kg{{s}^{-1}} $
B) $ 187.5kg{{s}^{-1}} $
C) $ 185.5kg{{s}^{-1}} $
D) $ 137.5kg{{s}^{-1}} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Given: Mass of rocket $ (m)=5000kg $
Exhaust speed $ (v)=800m/s $ Acceleration of rocket $ (a)=20m/s^{2} $
Gravitational acceleration$ (g)=10m/s^{2} $
We know that upward force $ F=m(g+a)=5000(10+20)=5000\times 30 $
$ =150000\text{ N} $
We also know that amount of gas ejected $ ( \frac{dm}{dt} )=\frac{F}{v}=\frac{150000}{800}=187.5kg/{{s}^{-1}} $
