In cycling races in which two (or more) riders pass the finish line almost simultaneously, you see these riders ‘push forward’ at the very last moment. Is this useful?

Answer

Yes, that is useful.
But let’s look at that for a moment, not as a stationary observer, but from a car that rides along with two sprinting riders. For simplicity, we assume that the riders cycle right next to each other, with an equal and constant speed, and that our car does the same. In front of us, both riders then stop, and it is the finish line that comes towards us. If neither jumps, the finish line will “hit” both front wheels at the same time.

But one cyclist is now going to jump, the other isn’t. The jumping cyclist actually consists of two “parts”, the bicycle and the rider himself. When he jumps, he pushes the bike forward opposite his body. Because this movement only takes place between the two “parts” and has no relation to the outside world, the center of mass, and thus the jumper as a whole, will still continue to travel at the same speed. Only his bike will now be slightly in front of the non-jumping bike, and his body slightly behind the body of the non-jumping colleague (see figure). The finish line will therefore now touch its front wheel first, and only then the front wheel of the non-jumping colleague. The effect is important because the bike weighs much less than the rider’s body. The bicycle is therefore pushed more forwards than the body is pushed backwards.

And in a sprint, every millimeter counts…