# Thread: Height from the ground will the child become airborne? picture included

1. ## Height from the ground will the child become airborne? picture included

A poorly designed playground slide begins with a straight section and ends with a circular arc as shown in the figure below

A child starts at point P and slides down both sections of the slide. At some point on the circular arc, the normal force goes to zero and the child loses contact with the ramp.
Assuming the forces of friction are negligible, at what height from the ground will the child become airborne?

I don't know where to start here!

2. centripetal force while on the circle is

$\displaystyle \frac{mv^2}{R} = mg\cos{\theta} - N$ where $\displaystyle \theta$ = angular position on the circle relative to the vertical.

contact is lost when $\displaystyle N = 0$ ...

$\displaystyle v^2 = Rg\cos{\theta}$

using energy ...

$\displaystyle 2g\Delta h = Rg\cos{\theta}$

$\displaystyle \Delta h$ = starting height above the circle's center $\displaystyle (4.8 m) - R\cos{\theta}$

solve for $\displaystyle \theta$ ... I get about $\displaystyle 35^\circ$