Question

A small spaceship whose mass is 2100 kg (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 13 kW laser beam, what speed will the ship attain in 4.0 days because of the momentum carried away by the beam?

Answer 1

The momentum of the light is equal (and opposite)to the momentum of the ship.

Momentum of light =   energy / c =   power * time / c

time is 4 day, or 345600sec so

   momentum = 13000 W * 345600 sec / 3.0 x 10⁸ m/s = 14.96 kg m/s

This is also the momentum of the ship after one day so

   momentum = m v

14.96 = 2100 * v

   v = 0.00712m/s = 7.12 mm/sec        is the speed of theship