Serway & Jewett — Conservation of Energy: Problem 33

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