Hello, I can\'t get this one to come out correctly, so any help is greatly appre

Question

Hello,

I can't get this one to come out correctly, so any help is greatly appreciated!

One of the contests at the school carnival is tothrow a spear at an underwater target lying flat on the bottom of apool. The water is 2.0m deep. You're standing on a small stool thatplaces your eyes 4.4m above the bottom of the pool. As you look atthe target, your gaze is 32 degrees below horizontal. Your raised armbrings the spear point to the level of your eyes as you throw it,and over this short distance you can assume that the spear travelsin a straight line rather than a parabolic trajectory.
At what angle below horizontal should you throw the spear in order to hit the target? Answer is two significant figures in degrees.

Thank you!

Explanation / Answer

The angle of glance is i = 32o The depth of water is d = 2.0 m The height of the observer above the water is h = 4.4 m - 2 m = 2.4 m Refractive index of water is n = 1.33 Apply Snell's law at the water-air interface sin(90-i) = nsin(90-r) cosi = ncosr cos32o = (1.33) cosr r = 50.38o From the laws of triangle D = h/tani     = 2.4 m / tan32o     = 3.84 m     = 3.84 m Also D' = d/tanr      = 2.0 m / tan50.38o      = 1.65 m Therefore the angle at which the spear to be thrown is = tan-1[(h+d)/(D+D')] = tan-1[4.4 m/5.49 m] = 38.7o      ˜39o      = 1.65 m Therefore the angle at which the spear to be thrown is = tan-1[(h+d)/(D+D')] = tan-1[4.4 m/5.49 m] = 38.7o      ˜39o      ˜39o

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