Problem A small mirror is attached to a vertical wall, and it hangs a distance of 1.99 m above the floor. The mirror is facing due east, and a ray of sunlight strikes the mirror early in the morning and then again later in the morning. The incident and reflected rays lie in a plane that is perpendicular to both the wall and the floor. Early in the morning, the reflected ray strikes the floor at a distance of 3.27 m from the base of the wall. Later on in the morning, the ray is observed to strike the floor at a distance of 1.06 m from the wall. The earth rotates at a rate of 15.0˚ per hour. How much time (in hours) has elapsed between the two observations?
Given data,
Height = 1.99 m
Distance = 3.27 m
Initial angle of incidence,
i = tan-1(1.99 / 3.27)
= 31.290
final angle of incidence,
f = tan-1(1.99 / 1.06)
= 61.860
angular displacement, theta =
f -
i
= 61.86 - 31.29
= 30.570
time elapsed =
/15 hours
= 30.57 / 15
= 2.038 hours
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