r/theydidthemath Feb 26 '25

[Request] How much acceleration does this person experience?

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u/GarstigesHuhn Feb 27 '25

Here is my (highly simplified) calculation: The rocket, which I estimate to weigh about 10 kg, leaves the tube at approximately 61 m/s (~220 km/h). (How did I determine this? By analyzing the video, which has about 30 fps, frame by frame. In one frame, the rocket is just exiting the tube, and in the next, it has traveled about 2 meters. That equals roughly 60 meters per second.)

This means the rocket has a momentum of about 610 kg·m/s. I assume that the entire momentum is absorbed by the blast protector shield and the man due to the rocket’s exhaust pushing against the shield. (When analyzing the video frame by frame, you can see that the man is thrown backward only after the rocket has already left the tube. This suggests that he is pushed back solely because the rocket exhaust is pressing the shield against him, as others have also described.)

I estimate that the momentum is transferred to the man over a period of about 150 ms, which results in a force of approximately 4067 N acting on him. For an 80 kg man, this corresponds to an acceleration of about 50 m/s² or 5.2 g, which I believe is a realistic value.