Question Detail
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/s², the amount of gas ejected per second to supply the needed thrust will be (Take g = 10 m/s²).
Correct Answer
Option D is the correct answer.
Detailed Explanation
Thrust F = v_exhaust × (dm/dt). Net upward force = Thrust - weight = m × a. So Thrust = m(g + a) = 5000 × (10 + 20) = 5000 × 30 = 150000 N. Then dm/dt = Thrust / v_exhaust = 150000 / 800 = 187.5 kg/s.
Hint
Thrust = v_exhaust × (dm/dt) = m(g + a).