Hmm... I'm not quite sure about that diagram as the blue trajectory, which lands in the pool, appears to be circular.

Ballistics, on Earth at least, is pretty straightforward. The lateral distance you travel just depends upon your lateral speed and the duration of your 'flight', with the duration of your 'flight' depending on how high you jump and how far you fall.

Working it out is pretty easy but you need to know the horizontal and vertical speed vectors at the point that you make the jump. Using your vertical speed you can work out how high you'll jump against gravity and for how long you'll be in the air until you hit the ground and you then just use this duration to work out how far you will have traveled in the horizontal direction, based on your horizontal speed. At the speeds you're likely to achieve by running, your slowdown due to air resistance will be negligible.

A long jumper, of the athletic type, not one of the neilp derived clothing items, sprints down the runway to maximise their horizontal speed and then tries to jump as high as they can.

For the simplest solution i.e. just running off the roof and not jumping up at all:

From

*s = ut + 1/2 at^2*where

*s* is displacement (20 ft),

*u* is initial speed (in this case 0 because we're just falling and not jumping up first),

*t* is the time and

*a* is acceleration (32.2 ft/s^2):

t^2 = s / (a / 2)

t^2 = 20 / (32.2 /2)

t^2 = 1.242

t= 1.114 seconds

So to travel 20 ft horizontally in a 20 foot drop you'll need to be moving at 20/1.114 feet per second = 17.952 fps = 12.24 mph

That would land you on the edge of the pool though, so you should probably add at least another five feet and use 25/1.114 = 22.441 fps = 15.300 mph.

Have a look at

http://en.wikipedia.org/wiki/SUVAT_equations#Relative_velocity and open up the two examples.

DO NOT TRY THIS EXPERIMENT BASED UPON MY MATHS