We start out sitting in our seats in the station, having just
boarded the train, looking at the rain as it falls straight down
from the sky. We're stationary, and the raindrops are falling at
60 kilometres per hour, their terminal velocity in the air. Now
the train pulls out of the station and begins to accelerate. As
it reaches 30 kilometers per hour, the view out the window looks
like: Even though the rain is still falling straight down, it
appears to be falling toward the train. The reason is obvious if
you think about; as each raindrop falls, we're moving toward it,
so we observe it to follow a slanted path, with the slant
increasing as we travel faster compared to the speed at which
the drop is falling. As the train reaches 60 kilometers per
hour, it's travelling as rapidly to the left, as seen from our
window, as the rain is falling from the sky. As a result, we see
the rain streaming toward us at an apparent angle of 45°--the
downward motion due to the rain's falling, the equal sideways
motion the resu