Question

What is the velocity of the canister relative to the Earth if the ship is heading directly away from the Earth?

a) 0.375c
b) 0.125c
c) 0.750c
d) 1.875c

Answer 1

The velocity of the canister relative to the Earth, if it is shot directly away from the Earth is 0.125c.

Step-by-step explanation:

In relativistic physics, velocities do not simply add up as they do in classical physics. To calculate the velocity of the canister relative to the Earth if it is shot directly away from the Earth, we can use the relativistic addition of velocities formula. Given that the spaceship is heading towards the Earth at 0.750c and the canister is shot at 0.500c relative to the ship, the velocity of the canister relative to the Earth can be calculated as:

V = (v1 + v2) / (1 + v1*v2/c^2)

where V is the velocity of the canister relative to the Earth, v1 is the velocity of the spaceship relative to the Earth, v2 is the velocity of the canister relative to the spaceship, and c is the speed of light.

Plugging in the given values:

V = (0.750c + (-0.500c)) / (1 + (0.750c*-0.500c)/(c^2))

Simplifying the expression:

V = 0.125c

Therefore, the correct answer is 0.125c (option b).