Bear Grylls has asked you to provide technical/scientific support for his cable

Question

Bear Grylls has asked you to provide technical/scientific support for his cable television show Man Versus Wild. This show features Bear teaching viewers survival techniques while stranded in remote locations. In one scene. Bear is demonstrating to viewers the skill of spear Fishing. While standing in a shallow river, Bear spots a fish. His first reaction is to aim directly at the fish, which would mean aiming at an angle = 43.40degree with respect to the vertical, as shown in the figure. However, Bear knows from experience that he can't throw the spear at the image because the actual location of the fish is closer to his feet than it appears, at a depth of H = 0.7000 m. This means he must shorten the angle at which he throws the spear. This slight decrease in the angle is represented as alpha in the figure. If Bear throws the spear at a height h = 1.050 m above the water, calculate the angle decrease alpha. Assume that the index of refraction for air is n_1 = 1.000 and that of water n_2 = 1.330 and that Bear aims the spear by pooring down its length.

Explanation / Answer

Sini /sinR = n2/n1

So Sin 43.4/ sinr = 1.33

So r = 31.1 degrees.

Now tan(43.4) = a/h

So a = 1.05*tan(43.4) = 0.9929

Similarly b = 0.7 * tan(31.1) = 0.4223

So Total length is 0.9929 + 0.4223 = 1.4152

Tan(phi-alpha) = d/h = L-d/H = L/ (h+H)

So Tan(43.4- alpha) = 1.4152/(1.05+7)

43.4 - alha = 38.96

So alpha = 4.44 degrees

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