Answer :
Answer:
1.35m
Explanation:
At the highest point of the jump, the vertical speed of the skier should be 0. So the 13m/s speed is horizontal, this speed stays the same from the jumping point to the highest point. The 14m/s speed at jumping point is the combination of both vertical and horizontal speeds.
The vertical speed at the jumping point can be computed:
[tex]v_v^2 + v_h^2 = v^2[/tex]
[tex]v_v^2 + 13^2 = 14^2[/tex]
[tex]v_v^2 = 196 - 169 = 27[/tex]
[tex]v_v = \sqrt{27} = 5.2 m/s[/tex]
When the skier jumps to the its potential energy is converted to kinetic energy:
[tex]E_p = E_k[/tex]
[tex]mgh = mv_v^2/2[/tex]
where m is the skier mass and h is the vertical distance traveled, [tex]v_v[/tex] is the vertical velocity at jumping point, and h is the highest point.
Let g = 10m/s2
We can divide both sides of the equation by m:
[tex]gh = v_v^2/2[/tex]
[tex]h = \frac{v_v^2}{2g} = \frac{27}{2*10} = 1.35 m[/tex]