This is all under the assumption that they are perfectly rigid bodies: A train i

Question

This is all under the assumption that they are perfectly rigid bodies:

A train is moving at 300m/s. A mosquito is moving directly towards it, head-on, at 4m/s.

When the mosquito and the train collide, the mosquito is at 0m/s, and then changes direction, moving at 300m/s in the direction of the train (because it's stuck to the windscreen).

Surely this says that, in theory, because there is a period of time where the mosquito is at 0m/s, the train must also be at 0m/s. But the train surely doesn't stop moving, and a mosquito certainly couldn't stop a train, even for the smallest amount of time.

Is this really what theory predicts? If not, where am I going wrong?
Is the theory flawed with this almost paradoxical situation?

Explanation / Answer

Mosquitos, windshields and trains are NOT perfectly rigid bodies.. In fact, the mosquito will suffer a completely inelastic collision with the windshield and will get squished when it hits. So the mosquito center of mass will gradually decrease from 4m/s to 0m/s and then to -300m/s and all of this will happen over the time frame of the squishing of the mosquito. During this same short time the windshield may change from 300m/s to 299.99999m/s (I made up this particular number, of course, I don't know how many 9s are needed) and back to 300m/s. This happens because even though the windshield seems like it is perfectly rigid, it really does have an elastic modulus so the windshield will very slightly deform as it applies the necessary force to decellerate and accelerate the squashed mosquito to the speed of the train. So this is what happens in reality and there is no problem - a finite but large force will act over a short distance (the squishing of the mosquito) to reverse the velocity of the mosquito. The train never decreases to 0 velocity.

What would happen if the mosquito, the train and the windshield really are perfectly rigid bodies? Well in that case, the large force that acted over a short time and distance would become an INFINITELY large force acting over an INFINITESIMALLY small time and distance that will give infinite acceleration to the mosquito which will cause a discontinuous change in the velocity of the center of mass of the mosquito so it will not spend anytime at all at zero velocity. And of course the train will not decrease to 0 velocity at all.

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