A small mirror is attached to a vertical wall, and it hangs a distance of 1.80 m

Question

A small mirror is attached to a vertical wall, and it hangs a distance of 1.80 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 3.86 m from the base of the wall. Later in the morning, the ray is observed to strike the floor at a distance of 1.26 m from the wall. The earth rotates at a rate of 15 degrees per hour. How much time (in hours) has elapsed between the two observations?

Explanation / Answer

Let the angle be p Therefore, tan p = 1.8/3.86 => p = 25o Final case: The height is still 1.8m but the base length is now 1.26m Let the angle be q Again, tan q = 1.8/1.26 => q = 55o Difference in angles = (55-25)o = 30o Therefore, time difference = 30/15 = 2hrs Thus, 2 hrs have elapsed between the two readings.

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