Question

How much energy is required to accelerate a spaceship with a rest mass of 120 metric tons to a speed of 0.481 c?

Answer 1

E = 1.51 × 10²¹ J

Step-by-step explanation:

Given:

Rest mass of the spaceship, m = 120 metric tonn = 120 × 10³ kg

Speed, v = 0.481 c

Now,

the relativistic kinetic energy required is calculated as:

`E=\frac{mc^2}{\sqrt{1-(v^2)/(c^2)}}-mc^2`

where, c is the speed of the light = 3 × 10⁸ m/s

on substituting the respective values, we get

`E=\frac{120*10^3*{c^2}}{\sqrt{1-((0.481c)^2)/(c^2)}}-(120*10^3*{c^2})`

or

E = 1.51 × 10²¹ J