A skier skis from rest from a vertical height h1 = 19.1 m over two successively lower hills of vertical heights h2 = 15 m and h3 = 5.2 m. (Fig. 7-30). The summit of the third hill fits a circle of radius h3 centered at height 0 m. Friction with the snow and air resistance are negligible.
(b) Does the skier leave the surface at x3?
Yes/No
If not, what should h1 be so that she just leaves the surface at x3? If yes, find the maximum value of h1 at which the skier stays on. (Ignore the middle hill in this calculation.)
_________m
so the skier does leave the surface at X3 but i don't know why.
100
To determine if the skier leaves the surface at x3, we need to compare the height of the third hill (h3 = 5.2 m) with the initial vertical height of the skier (h1 = 19.1 m).
If h1 > h3, then the skier does leave the surface at x3. This is because the skier has enough initial vertical height to reach the top of the third hill and go over it.
If h1 < h3, then the skier does not leave the surface at x3. This is because the skier does not have enough initial vertical height to reach the top of the third hill.
In this case, h1 = 19.1 m is greater than h3 = 5.2 m, so the skier does leave the surface at x3.
If we want the skier to just leave the surface at x3, we need to find the maximum value of h1 that allows the skier to barely reach the top of the third hill. In other words, we need to make h1 equal to h3.
Therefore, to find the maximum value of h1, we set h1 = h3 = 5.2 m. This means the skier has just enough initial vertical height to reach the top of the third hill without any excess.
So the maximum value of h1 at which the skier stays on is 5.2 m.