Question

An American ski jumper has a mass of 59.6 kg. He is moving at a speed of 23.4 m/s at a height of 44.6 meters above the ground. Determine the total mechanical energy of the jumper.

a. 4.42 x 10⁴ Jb. 4.24 x 10 ^-4 Jc. 4.24 x 10 ³ Jd. 42. 24 x 10⁴ J

Answer 1

Explanations & Calculations

• Mechanical energy is the sum of kinetic energy and potential energy.
• Therefore, the total energy he has right at that point is

$\qquad\qquad \begin{aligned} \small E_{total}&=\small mgh+\frac{1}{2}mv^2\\ &=\small m(gh+0.5v^2)\\ &=\small 59.6\,kg(9.8\,ms^{-2}\times44.6\,m+0.5\times(23.4ms^{-1})^2)\\ &=\small 42367.3\,J\\ &\approx\small 4.24\times10^4\,J \end{aligned}$