Question

A small mirror is attached to a vertical wall, and it hangs a distance of 1.87 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 3.56 m from the base of the wall. Later on in the morning, the ray is observed to strike the floor at a distance of 1.46 m from the wall. The earth rotates at a rate of 15.0o per hour. How much time (in hours) has elapsed between the two observations

Answer 1

t = 1.62 h

Step-by-step explanation:

A flat mirror fulfills the law of reflection where the incident angle is equal to the reflected angle.

θ_i = θ_r

If we use trigonometry to find the angles, the mirror is at a height of L = 1.87 m, and the reflected rays reach a distance x1 = 3.56 m

tan θ₁ = x₁ / L

tan θ₁ =
`(3.56)/(1.87)`

θ₁ = tan⁻¹ 1.90

θ₁ = 62.29º

for the second case x₂ = 1.46 m

tan θ₂ = x₂ / L

θ₂ = tan⁻¹
`(1.46)/(1.87)`

θ₂ = 37.98º

the difference in degree traveled is

Δθ = θ₁- θ₂

Δθ = 62.29 - 37.98

Δθ = 24.31º

as in the exercise they indicate that every 15º there is an hour

t = 24.31º (1h / 15º)

t = 1.62 h