The Galilean velocity transformation, Eq. 4-32, is so instinctively familiar from everyday experience that it is sometimes claimed to be \"obviously correct, requiring no proof.\" Many so-called refutations of relativity theory turn out to be based on this claim. How would you refute someone who made this claim?

The figure below shows the velocity vectors of the bus and the raindrops. It is assumed that the raindrops fall at an angle θ with respect to the vertical direction.

To the driver of the bus, the raindrops not only have the vertical velocity component but also a horizontal component, in a direction opposite to the direction of velocity vector of the bus. Therefore, the raindrops will appear to move in a direction at an angle θ relative to the vertical and given by:

It is important to note that θ is also the angle between the velocity vector of raindrops from the reference frame of the driver in bus and the velocity vector from the reference frame of the person on ground.