A vehicle lift capacity of 1500 kg satellite to polar orbit (700 km). The first stage is powered by a Pf-80 solid fuel rocket motor that delivers thrust 2261 KN for 108.6 seconds. The speed of the rocket at the end of the first stage is 1877 m/s at which time the Pf-80 rocket would have burned 88365 kG of fuel and teach an altitude of 40 Km.

The liftoff mass is 137 tonnes.

1- Find the rate at which the fuel is burned in the first stage, assuming a constant burn rate.

2-Find ver, speed of the exhaust relative to the rocket, assuming a constant burn rate

3- Find an expression for the power generated by the rocket, You may use the result that the energy output of the rocket engine is given by (1/2)(M0-M)(ver²) where M is the mass of the rocket at time t and Mo is the takeoff mass.

4- Estimate the work done against the force of gravity to get the rocket up to the altitude of 40 Km. Comment on how to obtain an accurate value for the work done against the gravity and provide an approximate expression