Fall from a horse

This September I fell from my horse while jumping. I decided to look into the physics behind it to find out how bad the fall was on paper compared to the actual outcome. The fall happened because my horse and I left the ground too far away from the jump and crashed through the top rails. We started with the velocity (in the x-direction) of 4.0 m/s and left from 2.0 m away to a 1.20 jump. At the top of the jump we experienced an inelastic collision with the stationary rails.

(702 kg)(4.0 m/s) +0=(702+18)V’

V’=3.9 m/s (x-direction)

After the crash I separated from my horse and fell at an estimated angle of 80 degrees. I was able to find the linear velocity at that angle to be 4.5 m/s and landed at a distance of 0.211 m from the jump. In addition to the linear motion I also rotated during the fall which contributed to my injuries. To find the F of the ground on me, I found KE energy of the linear and rotational motion and then used the work equation to find my acceleration. I then converted from m/s² to g’s and found that I was in the range to have obtained a concussion.

KE=(.5)(50.4)(5.82)²+(.5)(54)(4.5)²

KE=1399.68 J

W=∆KE               W=FdCosϴ       -1399.68=F(.211)Cos 80            F=38201

F=ma                38201=(54)a     a=707 m/s²                   72.2 g’s (70 to get a concussion)

For this problem I had to estimate quite a bit on the distances and velocity as well as the rotational numbers since the fall wasn’t recorded and I do not remember what happened. I also ignored air resistance and friction with the poles.