So this involves a little physics but it is to all be done using calculus (They give us everything we need). Everything is in terms of feet so acceleration due to gravity is 32 ft/(s^2) they tell us the mass of the jumper is 5 slugs. They then tell us that the Force due to the cord of bungee is Fc=0.39s where s is the length of the stretched part of the cord (basically just like the force of a spring). -L is the equilibrium point, basically where the bungee cord is at it's full length below the bridge but unstretched. Finally there is the force of air resistance but they just tell us it is proportional to the speed but in the opposite direction so Far= -v.
Problem 1: Let h=0 be the level of the bridge and fix our coordinate system so that the bottom of the gorge corresponds to h= -1053. At the instant the jumper reaches L feet below the bridge his height is h= -L. Let h<0 be the position of the jumper. As long as h<= -L, the total force F of the three forces on the jumper is F= -32m+0.39(-L-h)-v Find the acceleration where m=5 slugs.
Also we had three bungee cords to choose from, I chose the 415 ft cord where it's speed is 113 ft/s L feet below the bridge.
They then tell us that at t=0 is the time at which the jumper is L feet below the bridge.
Problem 2: For t>=0 let H(t) be the position of the jumper at time t, V(t) his velocity at time t, and A(t) be the acceleration at time t. What is H(0), V(0), and A(0)?
2. The attempt at a solution
Problem 1: I'm pretty sure I have this one I just want to start here and confirm my answers. The acceleration is denoted as a=(-32m+0.39(-L-h)-v)/m we can then plug in L and m (h and v are constantly changing) so a= (-321.85-0.39h-v)/5.
Problem 2: H(0)= -415 ft
V(0)= -113 ft/s
A(0)= -32 ft/s2
Please confirm these answers and then we can move on to the real calculus. Thanks!