A spotlight on a boat is y = 2.6 m above the water, and the light strikes the wa

Question

A spotlight on a boat is y = 2.6 m above the water, and the light strikes the water at a point that is x = 9.5 m horizontally displaced from the spotlight (see the drawing). The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light strikes the bottom.

________________ m

A spotlight on a boat is y = 2.6 m above the water, and the light strikes the water at a point that is x = 9.5 m horizontally displaced from the spotlight (see the drawing). The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light strikes the bottom.

Explanation / Answer

Set up triangles.

tan? = y/x

tan-1(2.6/9.5) = 15.30 degree

incident angle = angle from perpendicular = 90 - 15.30 =74.60 degree

n1sin?1 =n2sin?2

(1.0)(sin74.6) = (1.33)(sin?)

? = 46.45o

tan? = y/x

tan46.45 = y/4.0

y = 4.2 m

d = y + 9.5 = 4.2 + 9.5 =13.7 m

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