Question

The fictional rocket ship Adventure is measured to be 50 m long by the ship's captain inside the rocket.When the rocket moves past a space dock at 0.5c, space-dock personnel measure the rocket ship to be 43.3 m long. Part A The rocket ship Adventure travels to a star many light-years away, then turns around and returns at the same speed. When it returns to the space dock, who would have aged less: the space-dock personnel or ship's captain?

Answer 1

Time dilation occurs when an object moves at relativistic speeds, causing time to pass more slowly for the moving object. In this case, the space-dock personnel on Earth would have aged less than the ship's captain on the rocket.

Step-by-step explanation:

The phenomenon described in the question is called time dilation, which is a consequence of the theory of relativity. According to the theory of relativity, time passes more slowly for objects that are moving relative to an observer. In this case, when the rocket ship Adventure travels at a speed of 0.5c, which is half the speed of light, time dilation occurs. As a result, the space-dock personnel on Earth would have aged less than the ship's captain on the rocket.

Answer 2

Complete question:

Part A:) The fictional rocket ship Adventure is measured to be 50 m long by the ship's captain inside the rocket.When the rocket moves past a space dock at 0.5c , space-dock personnel measure the rocket ship to be 43.3 m long. The rocket ship Adventure travels to a star many light-years away, then turns around and returns at the same speed. When it returns to the space dock, who would have aged less: the space-dock personnel or ship's captain?

Part B: What is the momentum of a proton traveling at 0.62 c ?

Answer

a)Who would have aged less=The Captain would have aged less

b)
`p=3.96*10^(-19)kgm/s`

Step-by-step explanation:

From the question we are told that

Length measured by captain
`l_c=50m`

Speed of rocket past tje space dock
`V=0.5c`

Length measured by space-dock personnel
`l_c=43.3m`

a)

Generally time moves slower when moving at speed of light, due to time dilation or variation.

Who would have aged less=The Captain would have aged less

b)

Generally the equation for Relativistic Momentum is mathematically given as

`p=(m*v)/(1 - v^2/c^2)`

`p=(1.67*10^2-27*0.62*3.0*10^8))/(√( 1 -0.6^2))`

`p=3.96*10^(-19)kgm/s`