·| ... Cutnell, PhysicS, 10e A 68 4 k 9 bun e um gar i\"tanding on a tall platto

Question

·| ... Cutnell, PhysicS, 10e A 68 4 k 9 bun e um gar i"tanding on a tall platto m hu s0.3 m as i dicated in the ure The ban cord has natural le th of 8.10 m and, when stretched behaves1ike an ideal spring it spri him are Ns went 5nd-for the latter part of the descent, the elastic force of the bungee cord, what is his speed when he is at the following heights above the weter (a) 42.2 m, and (b) 15.1 m? constant er k 44.0N/m. The umpertalsfram rast, and it is ass medthat the only forces act ng on 0-8,10 vansion 4.24

Explanation / Answer

given, mass of bungee jumper, m = 68.4 kg

height of platform, ho = 50.3 m

natural length of the bungee cvord, Lo = 8.1 m

spring constant, k = 44 N/m

a. so at height ha = 42.2 m

extension in the length of the cord fro mits natural length = 50.3 - 42.2 - 8.1 = 0 m

hence, KE = potential energy lost

let the jumpers speed be u

then 0.5mu^2 = mgLo

u^2 = 2g*8.1

u = 12.606 m/s

b. at height 15.1 m

extension in length of the cord from its nbatural length = 50.3 - 15.1 - 8.1 = 27.1 m

stored PE in the string = 0.5k*27.1^2 = 16157.02 J

let the speed of the jumper be u

then

0.5*m*u^2 = mg(50.3 - 15.1) - 16157.02

u = 14.77147 m/s

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