Question

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20$m/s^{2},$ the amount of gas ejected per second to supply the needed thrust will be (Take g = 10 $m/s^{2}$)

• A. 127.5 kg/s
• B. 137.5 kg/s
• C. 155.5 kg/s
• D. 187.5 kg/s

Answer 1

The Correct Option is D

Given : Mass of rocket (m) = 5000 Kg
Exhaust speed (v) = 800 m/s
Acceleration of rocket (a) = 20 $m/s^{2}$
Gravitational acceleration (g) $=10 m/s^{2}$
We know that upward force
F = m(g +a) = 5000(10+20)
= 5000 x 30 = 150000 N.
We also know that amount of gas ejected
$\left(\frac{d m}{d t}\right)=\frac{F}{V}=\frac{150000}{800}=187.5 $ kg/s