When a man stands near the edge of an empty drainage ditch of depth 2.80 m, he c

Question

When a man stands near the edge of an empty drainage ditch of depth 2.80 m, he can barely see the boundary between the opposite wall and bottom of the ditch as in Figure (a) shown below. The distance from his eyes to the ground is h = 1.86 m. (Assume = 31.5°.) (a) What is the horizontal distance d from the man to the edge of the drainage ditch? d = Correct: Your answer is correct. . m (b) After the drainage ditch is filled with water as in Figure (b) shown above, what is the maximum distance x the man can stand from the edge and still see the same boundary? x = Incorrect: Your answer is incorrect. .

Explanation / Answer

a) tan theta = d/h

d = h tan theta = 1.86*tan(31.5 degrees)= 1,139  m

b) n sin theta = 1 sin theta2

theta2 = arcsin((1.33*sin(31.5 degrees))=44.02 degrees

so tan theta2 = x/h

x = 1.86*tan(44.02 degrees)= 1.79 m

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