Given:
The speed of the skier at the top of the first peak is,
[tex]v_1=3.0\text{ m/s}[/tex]The elevation of the slope is,
[tex]h_1=40\text{ m}[/tex]She skis down the slope to a valley with an elevation of 0.0 m and then glides to the peak of an adjacent slope that is at an elevation of
[tex]h_2=25\text{ m}[/tex]To find:
The speed at the second peak
Explanation:
The diagram can be depicted below as:
Using the conservation of the mechanical energy, we can write,
The total energy at peak 1 = The total energy at peak 2
So,
[tex]\begin{gathered} mgh_1+\frac{1}{2}mv_1^2=mgh_2+\frac{1}{2}mv_2^2 \\ v_2^2=2gh_1+v_1^2-2gh_2 \\ v_2=\sqrt{2gh_1+v_1^2-2gh_2} \end{gathered}[/tex]Substituting the values we get,
[tex]\begin{gathered} v_2=\sqrt{2\times9.8\times40+(3.0)^2-2\times9.8\times25} \\ =\sqrt{303} \\ =17.4\text{ m/s} \end{gathered}[/tex]Hence, the speed at the second peak is 17.4 m/s.
