Answer:
θ₁ = cos⁻¹ (n₁ / 2n₂)
Explanation:
For this exercise let's use the law of refraction
n₁ sint θ₁ = n₂. sin θ₂
Where n₁ and n₂ are the refractive indices for the two media, θ₁ and θ₂, the angles of incidence and refraction
They tell us that the angle of incidence is equal to the angle refracted over 2
θ₁ = θ₂ / 2
θ₂ = 2 θ₁
Let's replace
n₁ sin θ₁ = n₂ sin θ₂
Let's use the trigonometry relationship
sin 2θ = 2 sinθ cos θ
n₁ sin θ₁ = n₂ (2 sin θ₁ cos θ₁)
n₁ = n₂ cos θ₁
cos θ₁ = n₁ / 2 n₂
θ₁ = cos⁻¹ (n₁ / 2n₂)
Therefore, the angle of incidence is
θ₁ = cos⁻¹ (n₁ / 2n₂)
Answer:
a) 31.4 m/s
b) 50.2 m
Explanation:
a) When an object is free falling, its speed is determined by the gravity force giving it acceleration. Equation for the velocity of free fall started from the rest is:
v = g • t
g - is gravitational acceleration which is 9.81 m/s^2, sometimes rounded to 10
t - is the time of free fall
So:
v = 9.81 m/s^2 • 3.2
v = 31.4 m/s ( if g is rounded to 10, then the velocity is 10 • 3.2 = 32 m/s)
b) To determine the distance crossed in free fall we use the equation:
s = v0 + gt^2/2
v0 - is the starting velocity (since object started fall from rest, its v0 is 0)
s = gt^2/2
s = 9.81 m/s^2 • 3.2^2 / 2
s = 50.2 m (if we round g to 10 then the distance is 10 • 3.2^2/2 = 51.2 meters)
The real place should theoretically have space for 87 passengers if it is an exact model and doesn't have modifications in the seat numbers.
Because the molecules that move freely begin to compact closer together, with less heat, means less molecular activity.
