Grylls has asked you to provide technical/scientific support for his cable telev
ID: 1454149 • Letter: G
Question
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 theta = 43.4 degree 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 = 0.850 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 = 1.10 m above the water, calculate the angle decrease alpha. Assume that the index of refraction for air is n_1 = 1.00 and that of water n_2 = 1.33 and that Bear aims the spear by peering down its length.Explanation / Answer
This is a problem of refraction, whose expression
n1 Sin i = n2 Sin t
DAta
i = 43.4 deg
Sin t = n1 Sin i /n2
Sin t = 1/ 1.33 Sin 43.4
Sin t = 0.5166
t = 31.10 deg
As shown in Figure this is the beam pointing angle of the fish
Seek the distance x from the vertical to the fish, by trigonometria
Tan t = X2/H
X2 = H Tan t
X2 = 0.85 Tan 31.10
X2 = 0.513 m
We seek the horizontal distance X1 in the water surface
Tan i = X1/h
X1 = h tan i
X1 = 1.10 tan 43.4
X1= 1.040 m
We calculate the angle total respect to the vertical
X =X1 +X2
X = 1.040 + 0.513
X = 1.553 m
Y = 1.10 + 0.85
Y = 1.95 m
Tan = X/Y
Tan = 1.553/1.95
= 38.53 deg
You can observe the graph that the order angle is
= -
= 43.4 -38.53
= 4.87 deg
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