Wheatley

T = (2V*SinΘ)/g

X = V*CosΘ*T

V = Velocity
G = Gravity (9.8m/s)

LebeauHunter

Wheatley = smart.

statjunk

Good Job Wheatly. That is approximately 850 yards with the slower arrow. Imagine how compound bow technology could have changed war had someone figured it out back in the day. I thought it was interesting anyway.

Tom

Wheatley

Some of the old wood bows also shot long distances. They would make them as high as a pull they could get them and get big gorillas to shoot them.

I am not totaly sure it is correct. I did alot of this crap in physics in college but I could be wrong. Someone else verify the numbers and equations just to be sure.

Just don't shoot an arrow straight up, it is kinda dangerous.

BackwoodsBuck

*Edit: Just saw Wheatley beat me to it. Differences in numbers can be attributed to rounding differences.

1. How far will an arrow travel shot at a 45 degree angle at 285fps?

Separate velocity into x and y components.
Because angle is 45 degree
Vox^2 + Voy^2 = 285^2
Vox = 201.525
Voy = 201.525

Time of flight
Vfy = Voy + ay * (0.5t)
0 = 201.525 + (-32.2)*(0.5t)
t = 12.5171

horizontal distance
dx = Vox*t
dx = 201.525 * 12.5171
dx = 2522.2 ft total flight distance

2. How far will an arrow travel shot at a 45 degree angle at 310fps?

Same process as 1, different velocity
dx = 2984.47 ft total flight distance

3. How long will it take an arrow to hit the ground shot straight up at 285 fps?

Rise time
Vfy = Voy + ay * tr
0 = 285 + (-32.2)*tr
tr = 8.85093

total flight time
tf = 2*tr
tf = 2*8.85093
tf = 17.7019 seconds until the arrow hits the ground

4. How long will it take an arrow to hit the ground shot straight up at 310 fps?

Same process as 3, different velocity
tf = 19.2547 seconds until the arrow hits the ground

GMMAT

I've still got $20 that says some guy will swear he shoots 3" groups in all those scenarios.

statjunk

You're on. They'll say 2".

Tom

Wheatley

When I was young and dumb I shot an arrow not exactly straight up but pretty dawrn close. It came down on my neighboors roof and was sticking straight up in his roof. Needless to say I learned my lesson[&:] So I was speaking from expirience.

Thanks for verifying the numbers.

Backwoodsbuck = smart

Wheatley

I was just thinking! Couldn't someone just have played that bowman game (I think thats what it is called) where you adjust the angle and speed and try to hit the other guy. I can not remember is it told you the exact speed but if it did that would be an easy way to get the answer.

BackwoodsBuck

Next time I should read the replies before doing the work. It would probably save some time.