# Relativistic motion of the bullet

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1. Jun 8, 2015

### Caneholder123

1. A distant camera is taking an image of a bullet of proper length $l_0$ and velocity $v$. The bullet is moving on a straight line which is parallel to the ruler (a bit behind the bullet, when it is watched from the camera). An angle between the velocity vector and the line that connects the camera with the bullet is $\beta$. Determine the length of the bullet as seen from the camera, i.e. how much of the ruler is hidden.

2. Relevant equations
Lorentz transformations, from which the formula for the length contraction follows:
$$l=\frac {l_0}{\gamma}$$

3. The attempt at a solution
I just don't get this problem. Why is the angle $\beta$ given? Under the assumptions that the camera is far from the bullet and that the bullet is close to the ruler, isn't the length of the bullet measured just the contracted length? Angle $\beta$ will be changed, but I just can't see where it goes in this story.

2. Jun 8, 2015

### PWiz

Hint: length contraction always occurs along the direction of motion.

3. Jun 8, 2015

### Caneholder123

I didn't position the camera reference frame right. Thank you for the help.

4. Jun 8, 2015

### Sagar Singh

Do you know the answer bro??

5. Jun 10, 2015

### Caneholder123

No, m8. I don't get it. Doesn't the bullet move only move in x-direction in camera reference frame too, or I am not reading this properly? Sorry for being late with the reply, I was extremely busy last two days.

6. Jun 10, 2015

### Sagar Singh

actually there are many contradictions in this question, i think this is not complete question

7. Jun 10, 2015

### Caneholder123

Considering the approximations that the camera is far away from the bullet and that the bullet is right in front of the ruler, projection is just the length measured from the camera reference frame. And that length is $\frac {l_0}{\gamma}$ because the motion is just in one direction.

8. Jun 10, 2015

### Caneholder123

I realize that. Can you help me with the setup of the problem?

9. Jun 8, 2016

### BoGGoG

In case you're still wondering how to solve this: This exercise is from the "Problembook in Relativity and Gravitation" (Problem 1.5), see for example here:
http://apps.nrbook.com/relativity/index.html (need flash).

The key point is, that your camera measures the distance by receiving the photon from the front and from the back of the bullet simultaneously.
That means that the photon from the back of the bullet need so be sent earlier than from the front. In this time the bullet travels some length.

The solution is given in the book.