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How hard do you hit the ground when you fall? 1:45PM May 27, 2004 How Hard do you Hit the Ground when you Fall? This one's just for fun... How much harder do you hit the ground when bucked off, if: your horse is galloping instead of standing still? Come to think of it, what if you just fall right off? Or if the horse is galloping and you just slip off, is it a harder fall than getting bucked off standing still?
Okay, I've tried to keep this uncomplicated so far, but I'm going to make it into a 2 dimensional problem nowI apologize ;) vy_{impact} is the same in both situations; it's entirely dependent upon the height of the fall. vy_{impact}=g t_{fall} vx_{impact} for the standing buck is 0; for the galloping buck, it is v. v_{impact} = sqrt [(vx_{impact})² + (vy_{impact})²] When vx=0, then v_{impact}=vy. The force hitting the ground is again F=ma. In this case, the acceleration is: a_{impact}=(0v_{impact})/t_{impact} F_{impact}=ma > F=m(v_{impact}/t_{impact}) You can play along using the Javascript form at the bottom of the page. Okay, the only difference is in the "v_{impact}" term; can that really make a huge difference? Let's check. We have: m  weight of the person...say, 100 lb h  height of the horse...say, 15.2 (5.2 ft) v  speed the horse was going...initially, let's say he's standing still F_{buck}  force of the buck...say, 100 poundsenough to toss the rider 4 ft up above the horse's back t_buck  time the buck took (I'm assuming 1/2 second) g  gravity (32 ft/s²) I run it through a short Matlab program, and... The force of landing is 151 pounds. Now, let's say he was going 15 mi/hr (22 ft/s): The force of landing is 205 pounds. Yes, it makes a difference! But wait! Suppose that a running horse can't buck as hard as one standing still. Say, only half as hard (F_{buck}=50 lb  only enough to toss the rider up 1 foot): The force of landing is... 185 pounds. Okay, now say, you simply fall off the galloping horse (no bucking). So, say he was running all out and hit maybe 30 mi/hr (44 ft/s), and then F_{buck}=0. Now the force of landing is: 298 pounds! How does this compare to simply falling off a still horse? (aside from the embarassment factor): Force of landing: 114 pounds. How bad was YOUR worst fall? If you need to convert numbers, here's a good place to do it: http://www.onlineconversion.com/ 

