The one I learned was this: Person A is on a moving train and tosses a ball into the air of height H. To this person the ball travels a distance of 2H to in a

The one I learned was this: Person A is on a moving train and tosses a ball into the air of height H. To this person the ball travels a distance of 2H to in a time T to return to his hand. Person B is beside the tracks and sees the same event. To this person the ball travels 2 * (x^2 + H^2)^1/2, which we'll later call D, in the same time T where x is the distance the train traveled during this time. Since velocity is a measure distance divided by time the velocity of the ball in Person A's frame of reference is 2H/T (V1). The velocity of the ball in Person B's frame of reference is 2D/T (V2). Obviously V2 is greater because the distance traveled is greater for the same amount of time. Now suppose instead of tossing a ball into the air of height H, Person A shines a flashlight to a mirror at height H. The new constraint is this; the velocity of light is a constant and cannot be faster for Person B. Now what? Length contraction / time dilation is what.