To solve this problem we will resort to the concept of angle of incidence and refraction.
Since it is a reflection on a mirror, the angle provided for refraction will be equal to that of the incidence, that is, 25 °
The angle of reflation is always perpendicular to the surface so it is necessary to find the angle with respect to it.
Therefore the angle of the reflected beam of light made with the surface normal is 65°
Answer: The length of the shadow on the wall is decreasing by 0.6m/s
Explanation:
the specified moment in the problem, the man is standing at point D with his head at point E.
At that moment, his shadow on the wall is y=BC.
The two right triangles ΔABC and ΔADE are similar triangles. As such, their corresponding sides have equal ratios:
ADAB=DEBC
8/12=2/y,∴y=3 meters
If we consider the distance of the man from the building as x then the distance from the spotlight to the man is 12−x.
(12−x) /12=2/y
1− (1 /12x )=2 × 1/y
Let's take derivatives of both sides:
−1 / 12dx = −2 × 1 / y^2 dy
Let's divide both sides by dt:
−1/12⋅dx/dt=−2/y^2⋅dy/dt
At the specified moment:
dxdt=1.6 m/s
y=3
Let's plug them in:
−1/121.6) = - 2/9 × dy/dt
dy/dt = 1.6/12 ÷ 2/9
dy/dt = 1.6/12 × 9/2
dy/dt = 14.4/24 = 0.6m/s
