How does speed affect force? Like if a guy manages to jump 20

there's an x (forward) and h (upwards) component to his jump.
Call the jumping off speeds in those directions v_x and v_h.
His height as a function of time is
H(t) = t · v_h - t^2 · g/2
= t · (v_h - t · g/2)
where g is the gravitation acceleration on earth.
The time value T for which H(T)=0 is the time the guy is in the air:
T = 2·v_h / g
The distance he jumps is
T · v_x
= 2 v_x · v_h / g
This is linear in v_x (so doubling v_x doubles the distance) but quadratic in the total velocity v. If he jumps in the air more aggressively, he has more time and gets further.

If by force you mean air resistance, IIRC it scales v^2 for small velocity and v^3 for large.

>>8724761
>sin x = x = tan x

PHYSICS KEKS OUT OUT OUT OUT OUT OUT OUT REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Well, while he is in the air he has no force driving him forward, but he is opposed to the air resistance and his weight which pulls him to the ground.

It is his momentum that carries him through the air, momentum being calculated by mv=p where p is my boy's momentum in kgm/s, m is his mass and v is his velocity. So, answering your question, yes the distance he travels is directly proportional to his speed (through math which the guy up top kind of explains).

Any force that he may exert is on the ground when he hits it or if he hits anything mid-air.

Thanks amicae.