The royal gorge bridge over the arkansas river is 393 m above the river. a bungee jumper of mass 150 kg has an elastic cord of length 78 m attached to her feet. assume the cord acts like a spring of force constant k. the jumper leaps, barely touches the water, and after numerous ups and downs comes to rest at a height h above the water. the acceleration of gravity is 9.81 m/s². find h. answer in units of m.

188.7 m

Explanation:

height of bridge above water (h) = 393 m

mass of bungee jumper (m) = 150 kg

length of cord (L) = 78 m

acceleration due to gravity (g) = 9.8 m/s  

initial energy = mgh = 150 x 9.8 x 393 = 577,710 J

since the jumper barely touches the water, the maximum extension of the cord (x) = 393 - 78 = 315 m

from the conservation of energy mgh =

therefore

577,710 =

k = 11.64 N/m

from Hooke's law, force (f) = kx' ⇒ mg = kx'

where x' is the extension of the cord when it comes to rest

150 x 9.8 = 11.64 × x'

x' = 126.3 m

the final height at which the cord comes to a rest = height of the bridge - length of the cord - extension of the cord when it comes to rest

the final height at which the cord comes to a rest = 393  - 78 - 126.3 = 188.7 m

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.