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Classical Mechanics Level 3

Two astronauts are on the moon, they are \(1\) kilometer apart. One shouts to the other for help. As the astrounats can't communicate in space, the sound needs to be converted into radio signals.

Suppose it takes \(5 \times 10^{-2}\) seconds to convert the signals from sound to radio, and the same time is required to convert the radio waves back to sound. In the case above, the astronaut's sound gets converted to a \(100\) kilohertz wave of wavelength \(5\) centimeters.

To add another complication let's assume that it takes \(0.2\) seconds for the astronauts brain to interpret the sound. What is the total time required for the wave to reach the second astronaut?

Now, the second astronaut needs to reach the first astronaut to provide help. He runs with a speed of \(2\) meters per second. Only if he reaches the first astronaut within \(10\) minutes he will be able to help.

Add \(0.1\) seconds to the time taken for the wave to reach the second astronaut if he can accomplish the task. Subtract \(0.1\) seconds if he cannot accomplish the task. Input your answer accordingly.



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