Um... I will use kinematics to solve this.

The vertical component of the arrow is

The horizontal component of the arrow is

So, the time it takes to cover 200 ft is 200/58.9 = 3.40 s.

Now, use the formula

with t = 3.40,

u = 65.4 ft/s

a = -9.8 m/s^2 (you will have to convert to ft/s^2)

and solve for s.

If s < (40 - 4), then the arrow won't pass. Otherwise, it will.

What did you get?