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)

(a) 127.5kg/s

(b) 137.5kg/s

(c) 155.5 kg/s

(d) 187.5 kg/s

(d)

Given: Mass of rocket (m) = 5000 Kg Exhaust speed (v) = 800 m/s Acceleration of rocket (a) = 20 m/s²

Gravitational acceleration (g) = 10 m/s²

We know that upward force

F = m (g + a) = 5000 (10 + 20)  

= 5000 × 30 = 150000 N.

We also know that amount of gas ejected

:GivenMass of rocket(m)= 5000 kgExhaust speed(v)=800m/s^2   :FormulaAcceleration(a)=20m/s^2​v(dm/dt)=m(a+g)

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