Question

The local county fair this summer has a challenge with a winning prize of $250. You have to throw a spear at an underwater target that is sitting 1 meter below the water’s surface in a water trough. The challenge is arranged such that you have to stand on a platform that places your eyes 3 m above the bottom of the

trough (and therefore 3 vertical meters above the target). From your location, you see the target 30° below your horizon. At what angle below the horizontal should you throw the spear to directly hit the target? Assume your throw travels in a straight line.

Answer 1

you see the target 30° below your horizon . i.e . To hit the target you must throw at an angle below the horizontal line.

From geometry we find .

We know the refractive index of water is

If the refration angle is 'r', then using Snell's Law we find

Or

Given OL= 1m. We find

Given OM= 2m. We find

From geometry, we find QL=MS , PS=PM+MS=3.46+0.85=4.31M& QS= 3m .

from triangle, , we find

So at an angle 35⁰ below the horizontal you should throw the spear to directly hit the target.