Answer:
The distance between their eye and the ceiling is 33.06 m.
Explanation:
Given that,
The ceiling of a large symphony hall is covered with acoustic tiles which have small holes that are 4.35 mm center to center, D = 4.35 mm
Diameter of the eye of pupil, d = 5.1 mm
Wavelength, 
We need to find the distance between their eye and the ceiling. Using Rayleigh criteria, we get the distance as follows :
So, the distance between their eye and the ceiling is 33.06 m.
Answer:
cultural
Explanation:
Cultural anthropology studies the characteristics of the behavior learned in human societies, that is, science of human culture. In general, it is the science that studies the origin, development, structure, characteristics and variations of human culture in both past and present societies. Ethnography, ethnology, archeology, linguistics and physical anthropology are the disciplines on which cultural anthropology is founded.
Explanation:
The object is moving along the parabola y = x² and is at the point (√2, 2). Because the object is changing directions, it has a centripetal acceleration towards the center of the circle of curvature.
First, we need to find the radius of curvature. This is given by the equation:
R = [1 + (y')²]^(³/₂) / |y"|
y' = 2x and y" = 2:
R = [1 + (2x)²]^(³/₂) / |2|
R = (1 + 4x²)^(³/₂) / 2
At x = √2:
R = (1 + 4(√2)²)^(³/₂) / 2
R = (9)^(³/₂) / 2
R = 27 / 2
R = 13.5
So the centripetal force is:
F = m v² / r
F = m (5)² / 13.5
F = 1.85 m
Answer:
The impulse exerted by one cart on the other has a magnitude of 4 N.s.
Explanation:
Given;
mass of the first cart, m₁ = 2 kg
initial speed of the first car, u₁ = 3 m/s
mass of the second cart, m₂ = 4 kg
initial speed of the second cart, u₂ = 0
Let the final speed of both carts = v, since they stick together after collision.
Apply the principle of conservation of momentum to determine v
m₁u₁ + m₂u₂ = v(m₁ + m₂)
2 x 3 + 0 = v(2 + 4)
6 = 6v
v = 1 m/s
Impulse is given by;
I = ft = mΔv = m(
The impulse exerted by the first cart on the second cart is given;
I = 2 (3 -1 )
I = 4 N.s
The impulse exerted by the second cart on the first cart is given;
I = 4(0-1)
I = - 4 N.s (equal in magnitude but opposite in direction to the impulse exerted by the first).
Therefore, the impulse exerted by one cart on the other has a magnitude of 4 N.s.
