So this isn't a homework question, just something my brother-in-law asked me. He is in the Army, and wanted to know an approximate landing force he would experience when he lands. After attempting the problem, and looking things over, I realized it may be harder than once thought.
So, he told me he jumps from 1000ft (304.8m), and its a static line jump, so the parachute opens the instant he jumps from the plane. The total weight of him plus gear will be 300lbs (136.078kg), and he will fall at a CONSTANT velocity of 24ft/sec (7.3152m/s). From here, it was easy to calculate the time it would take him to reach the ground (41.667sec).
Initially I tried calculating acceleration with dv/dt, then realized if he has a constant velocity, there would be no acceleration, and therefore my plan of simply using a F=m*a would not work.
The Attempt at a Solution
From here, I then decided maybe it's more of a impulse-momentum type question as I would need to approximate an impact time, which he said maybe 0.5 seconds. Of course to make this easier, I will assuming he lands completely in the vertical, and not at an angle. Obviously his legs and body are going to be absorbing the force, and to calculate this doesn't appear to be straightforward.
I turned to the momentum equation p=m*v, and calculated his momentum being 995.379kgm/s. For the Impulse equation of F*t=m*dv or rearranging for F=(m*dv)/t. Using the approximated imapce time of 0.5 seconds, this give a force of 1.99kN. I have no idea what to reference this too, or if it is even a correct way of approaching the problem, so any help would be appreciated. Thanks!