"An especially interesting case arises when a projectile is hurled from the rear of a fast-moving train or other vehicle. Let us suppose that someone throws a stone, horizontally, down the track from the rear platform of a train speeding along at 60 miles per hour. And suppose that the stone is thrown at an initial speed of 60 miles per hour (relative to the train, of course) . Then, to the people on the train, the stone will appear to follow a perfectly normal parabolic path. But how will it seem to a person standing on the ground alongside the track? Remember that velocity is always relative. The forward motion of the train will just cancel the backward motion of the stone. In other words, the stone will plummet straight down to the ground, with no motion at all in the horizontal direction.
A similar situation arises when a bullet is fired from a speeding aeroplane. A revolver bullet, for instance, has a muzzle velocity of only about 500 miles per hour. If such a bullet is fired from the rear of a modern warplane speeding along at 500 miles per hour, the two velocities cancel, and the bullet at first stands still momentarily then falls straight down as though it had been dropped. On the other hand, if the bullet is fired from the front of the plane, the velocities add, and the speed of the bullet relative to the earth is 1,000 miles per hour. Of course, the machine guns used in warfare fire their bullets at speeds much greater than 500 miles per hour. Moreover, if the target is another moving plane, it is the speed of the bullet relative to this moving target that counts in determining the damage done not the speed relative to the earth. It makes no difference at all whether a revolver bullet stands still with respect to the earth and you run into it with a speed of 500 miles per hour, or whether you are standing still with respect to the earth and the revolver bullet strikes you with this speed. In both cases the effect is the same, and unpleasant for you."
From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena
By OVERTON LUHR