Relativity - Professor in spaceship examning students

[azatkgz]

And also check this one.

Homework Statement

A physics professor on the Earth gives an exam to her students.who are in the spacecraft traveling at a speed v relarive to the Earth.The moment the craft passes the professor,she signals to start of the exam.She wishes her students to have time interval $$T_0$$( spacecraft time)to complete the exam.Find the time interval T(Earth time) she should wait before sending a light signal telling them to stop.

The Attempt at a Solution

When in spacecraft $$T_0$$ for professor
$$T'=\frac{T_0}{\sqrt{1-\frac{v^2}{c^2}}}$$
$$T=T'-\frac{vT'}{c}=T_0\sqrt{\frac{1-v/c}{1+v/c}}$$

 

[MathematicalPhysicist]

seems alright by me, youv'e substracted the time it would take the signal to get to the spacecaraft from the overall time for the exam in the Earth's system.
nice work.

 

[m2003]

I would say that this is a great example of the concept of relativity. In this scenario, the professor on Earth and the students in the spacecraft are experiencing different time intervals due to their relative speeds. The professor observes the students' time interval, T_0, to be longer due to time dilation at high speeds. However, from the students' perspective, their time interval, T, is shorter due to length contraction. This is a fundamental concept in the theory of relativity, where time and space are not absolute but are relative to the observer's frame of reference.

To answer the question, the professor should wait for a time interval of T_0\sqrt{\frac{1-v/c}{1+v/c}} before sending the signal to stop. This is to ensure that the students have enough time to complete the exam according to their own time interval, T_0. This example highlights the importance of considering the effects of relativity in situations where objects are moving at high speeds relative to each other.