How do I calculate how much force a person is hit by someone swinging a backpack? I apologize for the odd videos, but they're for a physics project:
https://www.youtube.com/watch?v=b8n67-tHtEQ
In the video, a guy swings his backpack and hits a girl. What equation should I use to figure out how much force the girl was hit by when the guy swung the backpack? I can make whatever assumptions seems fitting.
Also, another question: I know the average velocity of a wrestler, but what should I do to find the initial velocity before running across the ring?
https://youtu.be/GBiPtakTv9s
Thanks for any help!
 A: To measure velocity you need a Δx, a measure of distance, and a Δt, a measure of the time interval, then v=Δx/Δt.
An impulsive force is Δ(p)/Δ(t) ,   a momentum over an estimated time interval . Momentum is m*v, so you need the mass(weight will do) of the backpack times the "instantaneous velocity when coming in contact with the victim. At the hit the momentum is transferred to the victim, that is the Δ(p), from 0 to the value of momentum carried by the backpack ( from conservation of momentum it will all go to the victim). That is the force the victim will feel. So you need the estimate of how long the impact lasts, the shorter the stronger the impulse.
A: You'll want to use the equation $F=ma$.
Assuming all the momentum of the moving backpack was absorbed by the girl, the force exerted on the girl would be the force the girl exerted on the backpack in order to cause it to stop. (If the girl absorbed all the momentum, all the sideways motion of the backpack would have stopped after she was hit (and the backpack would have moved directly downwards, acted on only by gravity). You can see in the videos that it still has some sideways momentum; maybe it was only a glancing blow. You can take this into account with some vector mathematics if you wish, but what I've written here is the basic approach.) The acceleration, $a$, can therefore be calculated from the duration of the impact $\Delta t$ and the velocity $v_i$ of the backpack upon impact. The final velocity $v_f = 0$, if you have assumed the entire impact was absorbed by the girl. So
$$a = \frac{v_f - v_i}{\Delta t}$$
You can estimate the initial velocity from the circumference of the swing, based on the length of the guy's arm (which becomes the radius of the backpack trajectory circle), $r$, and timestamps in the video. Maybe you can download it and use VLC or another media player to obtain very accurate (to milliseconds or better, I think) timestamps.
$$v_i = \frac{d}{t}$$
$$d = 2 \pi r$$
You may want to multiply $d$ by some fraction to represent the fraction of the circle circumference the backpack traced out between the two timestamps you've chosen, which you'll have to estimate visually, or maybe by drawing circles over the frames using Photoshop, GIMP etc. The $t$ in the previous equation is the time between these two timestamps, i.e. the time it took the backpack to cover this distance.
The mass of the backpack, $m$, can be estimated however you see fit. Perhaps you can weigh your backpack and the backpacks of a number of your friends and obtain an average value with uncertainty! :)

The initial velocity of a wrestler before they start running, i.e. when they are stationary, is $v_i = 0 \mathrm{\; m \cdot s^{-1}}$.
