A small mirror is attached to a vertical wall, and it hangs a distance of 1.76 m

Question

A small mirror is attached to a vertical wall, and it hangs a distance of 1.76 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 4.13 m from the base of the wall. Later on in the morning, the ray is observed to strike the floor at a distance of 1.15 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?

Explanation / Answer

Here, we need to find out the initial and final angles of reflection.

Initial case (Early Morniing) :
The height is 1.76 m and the base length is 4.13 m.

Let the angle be 1

Therefore, tan 1 = 1.76 / 4.13

=> 1 = 23.08o

Final case (Later in the Morning) :

The height is still 1.76 m but the base length is now 1.15 m

Let the angle be 2

Again, tan 2 = 1.76 / 1.15

=> 2 = 56.84o

Difference in angles = ( 2 - 1)

                              = (56.84o - 23.08o)

                              = 33.76 o

Therefore, time difference = 33.76 o / 15o

                                                = 2.25 hrs

Thus, 2.25 hrs have elapsed between the two observations.

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