That actually does sound pretty interesting, though I'm curious how you found a velocity with just a displacement
A bit of vector calculus. Math incoming!!!
An arrow fired from a bow has a constant horizontal velocity, and its vertical position follows a parabola with zeroes at time = 0 and time = when the arrow hits the ground (which is 300 m / horizontal speed) with leading coefficient g/2. I happen to know from physics that the best angle to fire a bow to get maximum distance is 45 degrees, so at t=0 the vertical and horizontal components of velocity should be equal. This information is enough to determine that an arrow fired 300 m at a 45 degree angle takes about 7.8 seconds, and has an initial velocity of about 54 m/s. Didn't consider the effects of atmosphere here. This works out to be about 183 feet/sec. Considering air would slow the projectile, in actuality slightly faster speeds are possible, but this information is good enough for my purposes.
Very first google result for "longbow speed" gave me 133.7ft/s
Though another result further down on the page says something about 150-180fps speed for bows as someone's preference... hell, wouldn't the value be highly variable from instance to instance?
Well, I wasn't the one manning the computer at the time, so I guess my roommate's googlefu is weak. And tho the value would be terribly variable from instance to instance, the goal of this exercise was to find a DC for an attempt to shoot an arrow with rope out of a pit, so working with "max range of a longbow is 300 m" is good enough.
Though ultimately I question the usefulness of all that math, as at the top of its height it'd have zero velocity and wouldn't even be able to penetrate anything with the rope.
Finding the max height is useful information is that max happens to be about 5 times less than the height of the pit the arrow was being fired out of in the first place. And again, the goal was to find the DC for a check, so max height is terribly useful info. If you're curious on how I found the max height, think conservation of energy.
Me, personally, with my own gaming style, I wouldn't have figured this all out (the only reason the guy actually running it bothered is that it's play by post. The reason I bothered is because it sounded like fun).
And now you see why I consider ability to use a microsoft program called Excel and the ability to do math to be different enough that the OP should have asked for help with excel, not with math. Personally, I am quite the novice at excel. If I need a glorified calculator I use mathematica. If I need a calculator, I have the one I bought in 1993.
