Answer
Chris' foot will be 52 meters below the bridge.
Work Step by Step
We can use conservation of energy to solve this question.
The gravitational potential energy at the top is transformed into elastic potential energy at the bottom:
$EPE = GPE$
$\frac{1}{2}ky^2 = mg(y+15)$
$\frac{1}{2}ky^2 - mgy - 15mg = 0$
$\frac{1}{2}(55 ~N/m)y^2 - (75 ~kg)(9.80 ~m/s^2)y - (15 ~m) (75 ~kg)(9.80 ~m/s^2) = 0$
$(27.5 ~N/m)y^2 - (735 ~N)y - (11025 ~J) = 0$
We can then use the quadratic formula to solve for $y$.
$y = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$y = \frac{735 \pm \sqrt{(-735)^2-(4)(27.5)(11025)}}{(2)(27.5)}$
$y = \frac{735 \pm 1324}{(55)}$
$y = 37 ~m, -11 ~m$
Since the negative value is unphysical, the correct answer is $y = 37 ~m$.
We can use $y$ to find the total distance $d$.
$d = y+15 = 37 ~m + 15 ~m = 52 ~m$
Chris' foot will be 52 meters below the bridge.
