# Plank and the bullet?

1. Feb 15, 2005

### Infamo

I dont know if you guys are fimiliar with this expiriment so I'll describe it first. Lets say that theres a plank(1km and at rest with respect to the plank) away, and I launch a bullet at the plank and 1,000km/sec, and exactly one second later, the bullet hits the plank. Now, the depth at which the bullet travels into the plank, is going to depend on its momentum. Now lets say that there is a space craft moving perpindicular to the bullets trajectory at very high speed(gamma factor of 10). The expiriment states, that the observer in the space craft is going to view the bullet taking 10sec to hit the plank instead of 1sec as observed by the stationary(with respect to the plank) observer because of time dialation(which I understand).

Now here are my questions.
1.) If your going 1,000km/sec, wouldn't it take alot less then 1sec to travel 1km.
2.) i thought that you can only experience time dialation and space concraction in parellel reference frames.

Keep in mind, i only started learning relativity 4-5weeks ago and I'm only a high school senior.

2. Feb 15, 2005

### sid_galt

It should take less than 1 s. It might be a misprint.

I think it is similar to the train-light experiment where a light beam is thrown vertically up in a carriage in a moving train. The observer in the train observes a straight line path while the observer outside the train moving with respect to train observes a slanted path of the light. You can calculate time-dilation via it.

Just replace the light with the bullet, remove the train and instead of it, move the platform. Time dilation will occur.

btw, length contraction will occur parallel to the direction of motion. Never heard of the time part though but I might be wrong.

Incidentally what are "parallel" reference frames. I haven't studied relativity much as I am only a sophomore in HS. Could you explain?

Last edited: Feb 15, 2005
3. Feb 15, 2005

### Crosson

For the observer at rest wrt (with respect to) the plank, the distance is one km and the bullets velocity is 1000m/sec and so the bullet strikes the plate in one second.

For the space ship observer, the distance is 1 km and the bullets speed is 1000m/s (you are correct about distances and velocities perpindicular to the motion not having relativistic corrections) so he sees the bullet hit the plank after 1 sec.

At the instant the bullet hits the plank, the observer on the ground sees his clock read 1 sec and the space ship clock read .1 sec (1/gamma factor [10]).

At the instant the bullet hits the plank, the observer in the spaceship sees his clock read 1 sec and the grounds observer's clock read .1 sec (1/gamma factor [10]).