Question

If a spaceship is approaching the Earth at 0.100c and a message capsule is sent toward it at 0.100c relative to the Earth, what is the speed of the capsule relative to the ship?

a) 0.200c
b) 0.000c
c) 0.100c
d) 0.300c

Answer 1

The speed of the capsule relative to the ship is 0.198c, which is approximately equal to 0.200c.

Step-by-step explanation:

The velocity of an object relative to another object can be found by using the relativistic addition of velocities formula.

In this case, the spaceship is approaching the Earth at 0.100c and the message capsule is sent toward it at 0.100c relative to the Earth.

The relativistic addition of velocities formula is given by:

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

Substituting the given values, we have:

v = (0.100c + 0.100c) / (1 + (0.100c * 0.100c) / c^2)

Simplifying the equation, we get:

v = 0.200c / (1 + 0.01) = 0.200c / 1.01 = 0.198c

Therefore, the speed of the capsule relative to the ship is 0.198c, which is approximately equal to 0.200c.