A skier starts at the top of a very large, frictionless snowball, with a very small initial speed, and skis straight down the side. At what point does she lose contact with the snowball and fly off at a tangent? That is, at the instant she loses contact with the snowball, what angle (alpha) does a radial line from the center of the snowball to the skier make with the vertical?

The answer to the question is

At the instant she loses contact with the snowball, the angle (alpha) a radial line from the center of the snowball to the skier make with the vertical is 48.2 °

Explanation:

At the point where the skier loses contact with the snpwball we have the centripetal force given by

m·g·cos θ - N =

Where  N = 0 at the point the skier leaves the snowball

That is

 m·g·cos θ  =

The height from which the skier drops from the snowball is given by

h = r - r·cosθ

Therefore the potential energy of the skier just before leaveing the snowball is

m·g·h = m·g·r·(1-cosθ)

From conservation of energy, the total energy of the skier is constant which means that is the potential energy is transformed to kinetic energy of the form

PE = KE That is  

= m·g·r·(1-cosθ) or

= 2·m·g·(1-cosθ) Howerver since   m·g·cos θ  = then we have

m·g·cos θ  = 2·m·g·(1-cosθ)  which gives

cosθ = 2·(1-cosθ) or 3·cosθ = 2

or cosθ =   and θ = = 48.1896851 °

≈48.2 °

i guess the game developers wanted to give off a more gamey/cartoony feeling without trying to copy fortnite exactly

the answer for apex is the lowest