An archer needs to hit a bull's-eye on target at eye level of 60 feet away is the archer fires the arrow from the eye level with a speed of 47 ft/s at an angle of 25 degrees above the horizontal, will the arrow hit the target

If the arrow covers a horizontal less than 60 feet, it will not hit the bull eye, but if it covers a horizontal distance of 60 feet it will hit the bull eye.

For a Projectile, the Range , R = U²Sin(2θ) / g

speed , U = 47 ft/s ,  g = 32.2 ft²/s,  θ = 25°

R =  U²Sin(2θ) / g

R =  47²Sin(2*25) / 32.2

R =  2209Sin(50) / 32.2 

R = 52.55

Hence range is 52.55 feet.

Since the range is less than the required 60 feet of the bull's eye, hence it will not hit the bull eye.