You are watching Olympic athletes practicing archery when you wonder how fast an

Question

You are watching Olympic athletes practicing archery when you wonder how fast an arrow is shot from a bow. With a flash of insight you remember your physics and see how you can easily determine what you want to know by a simple measurement. You ask one of the archers to pull back her bowstring as far as possible and shoot an arrow horizontally. The arrow strikes the ground at an angle of 86 degrees from the vertical at a distance of 100 feet from the archer. What is the answer to your query?

I was wondering if this problem could be solved with the range equation?

Also I didnt understand the part

v cos 86 = g x t
                            
                            t^2 = 30.48xcot 86 /g
                            t=0.466 sec

Can you write this out step by step?? Thanks for the help!

Explanation / Answer

so distance = v t

so 100 = vx*t

vx = 100/t

we know that tan(86) = vx/vy

and that vy = g*t

so tan(86) = (100/t)/(32*t)

t=0.467 s

so vx = 100/0.467=214.1 ft/s

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