At 220 m, the bungee jump at the Verzasca Dam in Locarno, Switzerland, is one of

Question

At 220 m, the bungee jump at the Verzasca Dam in Locarno, Switzerland, is one of the highest jumps on record. The length of the elastic cord, which can be modeled as having negligible mass and obeying Hooke's law, has to be precisely tailored to each jumper because the margin of error at the bottom of the dam is less than 10.0 m. Kristin prepares for her jump by first hanging at rest from a 15.0-m length of the cord and is observed to stretch the rope to a total length of 19.6 m. (a) What length of cord should Kristin use for her jump to be exactly 220 m? (b) What is the maximum acceleration she will experience during her jump? (Enter the magnitude.) m/s2 - Every answer to this first part of this question on chegg is wrong.

Explanation / Answer

GIVEN, h = 220 m

now, for a length of the cord, l = 15 m

length after kristing hangs from the rop, l' = 19.6 m

let her mass be m

then mg = k(l' - l) [ where k is spring constant of the rope]

m*9.81 = k(19.6 - 15) = k*4.6

m/k = 4.6/9.81 = 0.468

so before jumping h = 220 m

PE = mgh

if length of cord is l

then after the jump, PE stored in cord = 0.5k(220 - l)^2

hence

0.5k(220 - l)^2 = mg*220

0.5*(220 - l)^2 = 0.468*9.81*220

l = 175.054 m

a. hence she should use a cord of length l = 175.054 m

b. maximum acceleration be a

then

a = g - k(h-l)/m

a = 9.81 - (220-175.054)/0.468 = -86.2284 m/s/s

the -ve sign indicates that this acceleration is oppositre in direc tion to acceleration due to gravity

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