Chapter 8, Problem 33AP

Heedless of danger, a child leaps onto a pile of old mattresses to use them as a trampoline. His motion between two particular points is described by the energy conservation equation

$\frac{1}{2}(46.0\text{kg}){(2.40m/s)}^2+(46.0\text{kg})(9.80\text{m}/{\text{s}}^2)(2.80\text{m}+x)=\frac{1}{2}(1.94\times {10}^4\text{N}/\text{m})x^{{}^2}$

(a) Solve the equation for x. (b) Compose the statement of a problem, including data, for which this equation gives the solution. (c) Add the two values of x obtained in part (a) and divide by 2. (d) What is the significance of the resulting value in part (c)?