Achild slides down a slide on the playground and her hair starts to stand on end. what happened?

It's static electricity from sliding down. Whenever a person goes fast on something, (say a roller coaster/slide/etc...) their hair gets filled with static electricity. Have a good day! :3 

Possibly static electricity, I'm not so sure you should rely on my answer, but it's a guess.

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.