Question

A spacecraft has been designed to go to Mars's orbit to explore the plane. But for the time it has been put in the earth orbit, which is traveling at

a velocity of7.79 km/s. The spacecraft weighs 5 metric ton. Now the rocket needs to be put on an escape trajectory so that it can leave the earth orbit. Hence its engine is burned to accelerate it to a velocity of 12,000 m/s.The engine expels mass at a rate of 10 kg/s and an effective velocity of 3 km/s. Calculate the duration of the burn.

Fig: 1