Mapu sapling leaming ar Grylls has asked you to provide technical/scientific sup

Question

Mapu sapling leaming ar 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 = 43.4° 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 = 0.750 m. This means he must shorten the angle at which he throws the spear. This slight decrease in the angle is represented as in the figure image If Bear throws the spear at a height h = 1.20 m above the water, calculate the angle decrease . Assume that the index of refraction for air is n1.00 and that of water n21.33 and that Bear aims the spear by peering down its length Number Tools x 10

Explanation / Answer

at then point of refraction

using snells law

na sin A = nb sin B

A = phi = 43.4 deg

1 * sin (43.40 = 1.33 sin r

r = 31.1 deg

in trianlge ABR,

tan phi = BR/h

BR = h tan phi = 1.1 tan 43.4 = 1.04 m

in trianlge, tan r = EF/H

H tan r = 0.452

CF = CF + EF = BR + EF = 1.04 + 0.452 = 1.992

in ACF, tan (theta- alpha) = CF/AC = 1.992/h+H

tan (theta -alpha) = 1.992/1.85 = 0.8

alpha = 43.4 - 38.86 = 4.54 deg

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