A person named Larry is found dead, hanging at the 7-story level of a 15 story (45m) building. Larry has a mass of 90kg. When the bungee cord is cut, it has a relaxed length of 5 stories. Detective say he hit the ground while bungee jumping, you KNOW he was murdered. What is your evidence?
X(t)= Acos(wt + theta)
Fs=Fg when he's resting
The Attempt at a Solution
So at the 7 story level Fs=Fg if there's no acceleration. That's a change in X of 3 floors, or 9m. 90kg*9.8=9m*Ks
Know we know W= root (ks/mass), or 98/90, which gives me a w of 1.04
so X=A*cos(1.04T + theta)
I'd assume solving for A, or amplitude, from the resting point (7 floors up) would tell us if he hits the ground or not. If it's 21 or over, he hits it, if it's under, he clearly cannot hit the ground.
But, that's three unknowns.
So, I'm stuck, but just had an idea that I'm not sure is valid or not.
Using simple kinematics, if I were to choose 2 points, (say at 10m above and below the resting point), I could find the Avg. acceleration (Fg-Fspring)/mass, and knowing average acceleration and X position, I could solve for T.
Knowing T for X, I'd have two unknowns (A and theta) for two equations. I could then solve for A.
Would this be a correct line of thinking? Or am I erring somewhere? Thanks