Question

A Space ship of mass 5000 kg is heading towards the moon and wants to change its trajectory by 20 degrees relative to original path. The rocket has a velocity of 110 m/s. How much gas must be used up if it burns its rockets (using up fuel) and expels gas at a velocity of 1200 m/s (perpendicular to its direction of motion)?

Answer 1

given,

mass of the rocket = 5000 kg

velocity = 110 m/s ,angle = 20 degree

gases are expelled at speed = 1200 m/s

sideways velocity / radial velocity = tan(20)

Therefore the rocket will have a sideways momentum of

(M-m) * sideways velocity = (M-m) * radial velocity * tan(20)

where, M = initial rocket mass

m = mass of the gas expelled This sideways momentum will be balanced by the momentum of the gases expelled

m *1200 = (5000kg - m) *110* tan(20)

m*1200=200183.62 - 40.36*m

1240.36*m=200183.62

This gives

m = 161.43 kg

mass must be expelled = 161.43 kg