Question

A rocket ship 90 m long travels at constant velocity of 0.8C relative to the ground. As the nose of the rocket ship passes a ground observer, the pilot in the nose of the ship shines a flash bulb towards the tail of the ship. What time does the signal reaches the tail of the ship as recorded by 1. The ground observer 2. The pilot When does the tail of the rocket pass the ground observer? According to 1. the ground observer 2. According to the pilot

Answer 1

To calculate the time it takes for the signal from the flash bulb to reach the tail of the rocket ship, we use the time dilation formula. The time observed by the ground observer is calculated using the formula t' = t / √(1 - (v^2/c^2)), while the time observed by the pilot is simply the length of the rocket ship divided by the velocity. The time for the tail of the rocket ship to pass the ground observer is equal to the length of the ship divided by the velocity.

To calculate the time it takes for the signal from the flash bulb to reach the tail of the rocket ship, we need to consider the concept of time dilation due to special relativity. The time dilation formula is given by:

t' = t / √(1 - (v^2/c^2))

where t is the time observed by the ground observer, t' is the time observed by the pilot, v is the velocity of the rocket ship relative to the ground, and c is the speed of light.

Since the rocket ship is traveling at 0.8C (where C is the speed of light) relative to the ground and the flash bulb is stationary relative to the nose of the ship, the velocity v in the time dilation formula is 0.8C.

Using this formula, we can calculate the time it takes for the signal to reach the tail of the ship as:

t' = (90m / 0.8C) / √(1 - (0.8C)^2/C^2)

We also need to calculate the time it takes for the tail of the rocket ship to pass the ground observer. Since the rocket ship is 90m long, it takes 90m / 0.8C seconds for the tail of the ship to pass the ground observer.