Question

Marcia, an experienced bungee jumper, leaps from a tall bridge and falls toward the river below. The bridge is 155 feet above the water and Marcia's bungee cord is 80
feet long unstretched. When will Marcia's cord begin to stretch? Round your answer to two decimal places.

Answer 1

Answer:

Marcia's cord will begin to stretch after $2.24\:\rm{s}$.

Step-by-step explanation:

The expression used to find displacement is given as,

$s=ut+\dfrac{1}{2}at^{2}$

The initial velocity of Marcia before leaping is zero, so $u=0\:\rm{m/s^{2}}$.

Marcia travels under the influence of gravity and fall freely so the acceleration due to gravity is only acceleration responsible for her movement.

The value for $g$ is $10\:\rm{m/s^{2}}$(approximately) and when it is converted in $\:\rm{ft/s^{2}}$, it is $32\:\rm{ft/s^{2}}$.

Substituting the values, the distance that Marica travels under influence of gravity for $t$ seconds is,

$\begin{aglined}s&=ut+\dfrac{1}{2}at^{2}\\s&=(0)t+\dfrac{1}{2}gt^{2}\\s&=0+\dfrac{1}{2}(32)t^{2}\\s&=16t^{2}\end{aligned}$

The bungee cord begins to stretch after Marcia has fallen $80\:\rm{ft}$, so

$\begin{aligned}s&=16t^{2} \\80&=16t^{2} \\t^{2} &=5\\t&=2.24\:\rm{s}\end{aligned}$