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^{3}kg. On ignition, gas is ejected from the rocket at a speed of 2.5 X 10

^{3}m/s relative to the rocket, and fuel is consumed at a constant rate of 7.4 kg/s. Find the thrust of the rocket.

Can someone please check my solution?

Let the mass of both the rocket and fuel be m, and let T be the thrust. Let 'a' be the acceleration of the rocket, and g be the acceleration due to gravity. Then,

[tex]T = \frac{d(mv)}{dt} [/tex]

[tex]T = m\frac{dv}{dt} + v\frac{dm}{dt}[/tex]

[tex]T = 7.4 kgs^{-1} \times 2.5 \times 10^3 ms^{-1}[/tex]

[tex]T = 19.5 \times 10^3 N[/tex]