While the principle is fairly straightforward, this video is such an endearing representation of the concept of relative motion that we had to share it. Who wouldn't appreciate the lengths they went to do the demonstration, not to mention the dramatic atmosphere of the video!
Now, for those of you who aren't fluent in Japanese, let's present the question in (rough) translation: If a truck is moving forward at a speed of 100 km/hr, and you launch a ball off the back end with a speed of 100 km/hr relative to the truck, what is the motion of the ball relative to the ground?
In a perfect demonstration the ball will have exactly zero lateral motion, and therefore will fall exactly straight down to the ground! To figure the velocity relative to an observer on the ground we simply need to realize that the forward motion of the car is perfectly offset by the backward motion of the ball. Mathematically:
v(ball relative to ground) = v(car relative to ground) + v(ball relative to car)
where the velocity of the ball is negative in this case. This logical addition of velocities is called a "Galilean transformation". Watch the final slow motion replay in the video. The ball almost does fall straight down. It retains just a little bit of forward velocity, which means that the launch speed of the ball must have been slightly less than the speed of the car. If you look closely it also seems to have a bit of forward "kick" after hitting the ground due to the rotation of the ball. But physics experiments are never perfect. Well done!
(A final but not insignificant note: The "Galilean transformation" is very logical, conforms to common sense, and applies to every situation you are ever likely to encounter. It does not apply, though, at very high velocities—as in, close to the speed of light! In those cases we need to resort to Einstein's Theory of Special Relativity, which does not necessarily conform to common sense. But that's a story for another video.)
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.