Rocket Exhaust Gases: Initial & After 29s Acceleration

[sloanmp]

A rocket with initial mass of 7.30×103 kg is fired in the vertical direction. Its exhaust gases are ejected at the rate of 6.00×101 kg/s with a relative velocity of 2.100×103 m/s. What is the initial acceleration of the rocket? What is the acceleration after 29 s have elapsed?

 

[Redsummers]

A rocket with initial mass of 7.30×103 kg is fired in the vertical direction. Its exhaust gases are ejected at the rate of 6.00×101 kg/s with a relative velocity of 2.100×103 m/s. What is the initial acceleration of the rocket? What is the acceleration after 29 s have elapsed?

I think you will first need to find such a thing like the Thrust of the rocket, which can be obtained by:

$$F_s dt = dm\cdot\vector{v}_r$$

With the thrust, which is clearly a force, you can solve for F =ma, m being the initial one (take into account that your rocket is losing mass as it goes up).
Hint: The total force is the thrust + the gravity!