The answers here are all using newtonian physics. We are not using relativity here. And you DO NOT want to. Relativity will twist your mind into a knot.

1. pick two known points on the track beside the train. Say the start of a tunnel, bridge, etc. Two experimenters with synhronized watches. One sites in the 1st car, the second sits in the second car. Note the time the first point appears at your windows. The second person then gets up and walks to the front of the train. Note the time the 2nd point appears at your windows. Measure the distance between the two points. Work out the speed.

2. Don't jump. Throw a rock out the window. It might be easier to do this on a car. Drop a rock from your left hand, throw the one on the right. Release at the same time. Measure with a tape.

3. Do the same experiment as (2). Mark out distances on the road. Have some one record it with a camcorder. Examining the video frame by frame. You should be able to work out the speed.

Have i just done your homework for you?

This post has been edited by dkk: Sep 17 2010, 08:46 AM

It will land back on the canon itself. At point 0.0. You can test this yourself with a little toy canon that shoots the ball only 2m up.

Or even simpler. Hold a ball over a spot on the floor of the train. Let it go. It will fall straight down and hit the spot.

Air resistance does not enter the equation because the train is sealed. Close all the windows and doors before doing your experiment.