(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Relative to the rest frame, the trajectory of a space ship is:

[tex]x=vt[/tex]

[tex]y=y_0[/tex]

An observer at:

[tex](x,y)=(0,0)[/tex]

wants to send a photon to hit the spaceship at:

[tex](x,y)=(0,y_0)[/tex]

a) When and in what direction must the observer send the photon?

b) In the frame of the spaceship, what is the angle between the spaceship and the photon's velocity?

2. Relevant equations

Basic velocity to distance relations. Possibly Lorentz transformation?

3. The attempt at a solution\

a) Well, the observer is trying to send a photon from (x,y)=(0,0) to (x,y)=(0,y_{0}); therefore he muse send it in the +y-direction. The time it takes the photon to reach (x,y)=(0,y_{0}) is:

[tex]t=\frac{y_o}{c}[/tex]

Since the spaceship is moving in the +x-direction at speed v, the observer must send the photon when the spaceship is at:

[tex]x=vt=\frac{-vy_o}{c}[/tex]

b)This part is hard and I have made a few arguments that lead to different paths:

Which one of my argument is valid?

- The speed of the spaceship in the spaceship's frame is zero, then how could there be an angle?
- When the photon strikes the spaceship, the photon only has a y velocity while the spacecraft has only a x velocity. Therefore, the angle is 90 degrees.

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# Shooting a spaceship with a photon

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