A small spaceship with a mass of only 2.6 ✕ 103 kg (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 12 kW laser beam, what speed will the ship attain in 1.0 day because of the momentum carried away by the beam?

v = 2.66 10⁻³ m/s

Explanation:

To work this problem we must use the relationship between the amount of movement and energy for an electromagnetic wave

p = U / c

They give us the power of the laser, which is the relationship between work and time. Work is the variation of energy, in a laser beam that is an electromagnetic wave. We have its power

P = W / t

W = P t

Work is the variation of energy W = U

p = P t / c

½ m v = P t / c

v = 2 P t / m c

Let's reduce time to SI units

t = 1.0 day (24 h / 1 day) (3600 s / 1 h) = 86400 s

Let's calculate

v = 2 12 10³ 86400 / (2.6 10³ 3 10⁸)

v = 2.66 10⁻³ m / s