Since it is a U-shaped pool, it can be assumed that it is a parabola passing through the origin Y = AX 2.

And assuming that the U-shaped pool is absolutely smooth, there is no friction and no energy loss during the sliding process, the height is h0, and the final flying height is H.

We know that the derivative of this parabola is y'=2ax. Suppose the athlete flies out at the height y0.

According to the conservation of energy, the flight speed is v, that is,1/2mv 2 = mg (h0-y0), and the tangent of the direction angle is 2A * ((y0/a) under the radical formula =-2 ((ay0) under the radical formula).

Then it is obtained from the conservation of energy: mgh= 1/2m (V *(2(Ay0))2 = 2mv 2 * a * y0 under the radical formula.

The result is: mgh=4mg(h0-y0)*a*y0.

h=4a(h0-y0)*y0

Derive the above formula. Make its derivative zero. Y0= 1/2h0 is obtained.

So fly out at half the height of the slide.