Question

A 2,000-kg spacecraft has an initial velocity of 8 km/s. A thruster is then fired which provides a thrust force of 10,000 N for 15 seconds. What is the velocity of the spacecraft after the thruster burn? (assume a straight path)

Answer 1

Given that :

mass of the spacecraft, m = 2000 kg

initial velocity of spacecraft, v_o = 8 km/s = 8000 m/s

thrust force, F = 10,000 N

time taken, t = 15 sec

Using newton's second law of motion -

F = m a                                                                             { eq.1 }

inserting the values in above eq.

(10,000 N) = (2,000 kg) a

a = 5 m/s²

Velocity of the spacecraft after the thruster burn which will be given as :

using equation of motion 1,

v = v₀ + a t                                                                                  { eq.2 }

inserting the values in eq.2,

v = (8000 m/s) + (5 m/s²) (15 s)

v = 8075 m/s

m/s convert into km/s :

v = 8.07 km/s