Question

In recent years, the Nike vaporfly running shoes have caused a stir in the world of high-performance marathon running. The shoes, as can be seen in the picture at right, are significantly thicker than conventional running shoes. They have a special midsole that is exceptionally squishy. Imagine a 70-kg runner is wearing the vaporfly shoes. At the top of his stride (when his center of mass is at its farthest point above the ground), his speed is 10 m/s.

a. At the bottom of his stride, but before the midsole of his shoe compresses, the runner’s center of mass is 10 cm closer to the ground than it was at the top of his stride. What is his speed at the bottom of his stride? Show your work

Answer 1

The speed at the bottom of the stride can be calculated by adding the gained potential energy to his inital kinetic energy to find his final kinetic energy

$K_{f}=\frac{1}{2}mv_i^2+mg\Delta h$

$K_{f}=\frac{1}{2}\times 70\times 10^2+(70\times 9.81\times 0.1)=3568.67\mathrm{J}$

We know that

$K_{f}=\frac{1}{2}mv_f^2$

Equating the two, we get

$\frac{1}{2}mv_f^2=3568.67$

$\frac{1}{2}\times 70\times v_f^2=3568.67$

$v_f=10.098\mathrm{m/s}$