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 = 1.95 m. (Assume theta = 31.8 degree.) (a) What is the horizontal distance d from the man to the edge of the drainage ditch? d = (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 = Your from the correct answer by more than 10%. Double check your calculations.

Explanation / Answer

for drainage ditch ,

tan(theta) = d / h

d = h tan31.8 = 1.95 x tan31.8

d = 1.21 m ....Ans(A )

(B) When filled with water,

Applying snell's law,

ni sin(i) =nr sin(r)

1.33 sin(31.8) = sin(r)

r = 44.5 deg

and tan(r) = x / h

x = 1.95 tan(44.5)

x = 1.92 m .........Ans

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