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

 t = 1.62 h

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 =

         θ₁ = tan⁻¹  1.90

         θ₁ = 62.29º

for the second case x₂ = 1.46 m

        tan θ₂ = x₂ / L

        θ₂ = tan⁻¹  

        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

low freq = 100 mhz

low wavelength =101.7m

length = 3x10^8/freq

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min