Question

It's your birthday, and to celebrate you're going to make your first bungee jump. You stand on a bridge 100m above a raging river and attach a 35-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 43N/m . Assume that your mass is 79kg . After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation? h=

Answer 1

Answer:

h = 47 m

Explanation:

First, we will calculate the force on the cord due to the weight:

$Force = F = Weight\\F = mg\\F = (79\ kg)(9.81\ m/s^2)\\F = 775\ N$

Now, we will calculate the elongation by using Hooke's Law:

$F = k \Delta x$

where,

k = spring constant = 43 N/m

Δx = elongation = ?

Therefore,

$775\ N = (43\ N/m)\Delta x\\\\\Delta x = \frac{775\ N}{43\ N/m}\\\\\Delta x = 18\ m$

So, the final length of the cord will be:

$Final\ Length = Initial\ Length + \Delta x\\Final\ Length = 35\ m + 18\ m\\Final\ Length = 53\ m$

Hence, the height from water (h) can be found using the following formula:

$h = Height\ of\ Bridge - Final\ Length\ of\ cord\\h = 100\ m - 53\ m$

h = 47 m