Question

Imagine you are riding on a yacht in the ocean and traveling at 20 mph. You then hit a golf ball at 100 mph from the deck of the yacht. You see the ball move away from you at 100mph, while a person standing on a near by beach would observe your golf ball traveling at 120 mph (20 mph + 100 mph).
Now imagine you are aboard the Hermes spacecraft traveling at 0.1c (1/10 the speed of light) past Mars and shine a laser from the front of the ship. You would see the light traveling at c (the speed of light) away from your ship. According to Einstein’s special relativity, how fast will a person on Mars observe the light to be traveling?


A) 0.1c (1/10 the speed of light)

B) c (the speed of light)

C)1.1c (c+0.1c)

Answer 1

According to Einstein's special theory of relativity, the speed of the light in a vacuum is the same no matter the speed with which an observer travels. So the answer should be A) 0,1c (1/10 the speed of light)

Answer 2

Answer:

B) c (the speed of light)

Explanation:

Adding the velocities of the golf ball and the boat is fine in the classical sense.

But the light photons are not bound by the rules of classical dynamics.

Einstein postulated that the speed of light is constant in every frame of reference, irrespective of the speed of the observer. It is the maximum velocity at which an object can move.

So the laser would appear to move at the speed of light for an observer inside the Hermes spacecraft and to the observer on mars.

It is because, inside the Hermes time will be slowed down to make sure nothing moves faster than light. This is called time dilation

let $T_{o}$ be the time measured inside Hermes,

Time outside Hermes

$T = \frac{T_{o}}{\sqrt{1-\frac{v^{2} }{c^{2} } } } \\\\T = \frac{T_{o}}{\sqrt{1-\frac{(0.1c)^{2} }{c^{2} } } } \\\\T = 1.005T_{o}$

So 1 second inside Hermes is as long as 1.005 seconds outside Hermes, so the laser would appear to travel at the speed of light to observers outside and inside Hermes.