# Special relativity problems

• dumbperson
In summary, the question is about two planes flying with the same speed and having two identical clocks on board. The first part asks about the time it takes for a radio signal to reach the second plane based on the clock on board the second plane. The second part asks about the time it takes for the signal to reach the second plane based on the clock at the control tower. Equations for time dilation and length contraction are provided, but the solution is not clear.

## Homework Statement

Two planes are flying (one behind the other) with the same speed v with respect to the ground, and they have two identical clocks on board.
The distance between the planes is determined on x_1 (they don't mean the distance measured is equal to x_1 do they..?). On t=0 (according to the clock on board of the front plane) the pilot sends a radiosignal to the plane behind him.

1.

On what time t_1 does this signal reach the second plane according to the clock on board of the second plane?

2.

On the instant that the signal is being emitted, the front plane is right above the control tower, and the clock of the control tower shows the same time t'=0. On what time t_1 ' does the second plane receive the signal according to the clock on the control tower?

## Homework Equations

$$t'= \frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}$$
$$x'=\frac{x-vt}{\sqrt{1-v^2/c^2}$$
$$\Delta t = \frac{\Delta t'}{\sqrt{1-v^2/c^2}}$$
$$L'=L\sqrt{1-v^2/c^2}$$

## The Attempt at a Solution

1.

If the measured distance between the two planes is L, I would think that
$$t_1 =\frac{L/c}$$ because they are going with the same speed relative to the ground, is this correct?

2.

Here I am lost, is this not simply
$$t_1'= \frac{t_1-vL/c^2}{\sqrt{1-v^2/c^2}}$$ ?

I am really lost, could I have a tip?

thank you!

I thought about it again and I thought it could be

$$t_1'=\gamma t_1$$ , but again I'm not really sure, because the plane is moving towards the radiosignal(so we have a radiosignal going towards the plane with velocity c and the plane going towards the signal with velocity v) and I don't really know how to deal with this.

Anyone?