A $50\mathrm{.}0-$kg bungee jumper steps off a bridge with a light bungee cord tied to her and to the bridge. The unstretched length of the cord is $14\mathrm{.}0$ m$.$ The jumper reaches reaches the bottom of her motion $38\mathrm{.}0$ m below the bridge before bouncing back. We wish to find the time interval between her leaving the bridge and her arriving at the bottom of her motion. Her overall motion can be separated into an $14\mathrm{.}0-$m free$-$fall and a $24\mathrm{.}0-$m section of simple harmonic oscillation.

$($a$)$ For the free$-$fall part, what is the appropriate analysis model to describe her motion.

particle under constant angular accelerationparticle in simple harmonic motion$$particle under constant acceleration

$($b$)$ For what time interval is she in free$-$fall?

s

$($c$)$ For the the simple harmonic oscillation part of the plunge, is the system of the bungee jumper, the spring, and the Earth isolated or non$-$isolated?

isolatednon$-$isolated$$

$($d$)$ From your response in part $($c$)$ find the spring constant of the bungee cord.

N$/$m

$($e$)$ What is the location of the equilibrium point where the spring force balances the gravitational force exerted on the jumper?

m below the bridge

$($f$)$ What is the angular frequency of the oscillation?

rad$/$s