Question

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?

Answer 1

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