Question

A small spaceship whose mass is 1300 kg (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 11 kW laser beam, what speed will the ship attain in 4.0 days because of the momentum carried away by the beam?

Answer 1

Step-by-step explanation:

Relation between energy and momentum is as follows .

E = h c / λ

E / c = h / λ

h /λ = momentum of a photon

momentum of a photon = E /c

= 11 x 10³ / 3 x 10⁸

= 3.67 x 10⁻⁵

In 4 days no of photon

= 4 x 24 x 60 x 60 = 345600 .

momentum of photon released

3.67 x 10⁻⁵ x 345600 .

= 12.68 kg m/s

This momentum will be imparted to spaceship .

12.68 = mv

12 .68 = 1300 x v

v = .00975 m /s

= 9.75 mm /s