Question

A water skier lets go of the tow rope upon leaving the end ofa

Answer 1

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:

$v_v^2 + v_h^2 = v^2$

$v_v^2 + 13^2 = 14^2$

$v_v^2 = 196 - 169 = 27$

$v_v = \sqrt{27} = 5.2 m/s$

When the skier jumps to the its potential energy is converted to kinetic energy:

$E_p = E_k$

$mgh = mv_v^2/2$

where m is the skier mass and h is the vertical distance traveled, $v_v$ 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:

$gh = v_v^2/2$

$h = \frac{v_v^2}{2g} = \frac{27}{2*10} = 1.35 m$