Explanation:
We need to calculate the speed of light in each materials
(I). Gallium phosphide,
The index of refraction of Gallium phosphide is 3.50
Using formula of speed of light
....(I)
Where, 
= index of refraction
c = speed of light
Put the value into the formula
(II) Carbon disulfide,
The index of refraction of Gallium phosphide is 1.63
Put the value in the equation (I)
(III). Benzene,
The index of refraction of Gallium phosphide is 1.50
Put the value in the equation (I)
Hence, This is the required solution.
From an energy balance, we can use this formula to solve for the angular speed of the chimney
ω^2 = 3g / h sin θ
Substituting the given values:
ω^2 = 3 (9.81) / 53.2 sin 34.1
ω^2 = 0.987 /s
The formula for radial acceleration is:
a = rω^2
So,
a = 53.2 (0.987) = 52.494 /s^2
The linear velocity is:
v^2 = ar
v^2 = 52.949 (53.2) = 2816.887
The tangential acceleration is:
a = r v^2
a = 53.2 (2816.887)
a = 149858.378 m/s^2
If the tangential acceleration is equal to g:
g = r^2 3g / sin θ
Solving for θ
θ = 67°
Answer:
a. Final velocity, V = 2.179 m/s.
b. Final velocity, V = 7.071 m/s.
Explanation:
<u>Given the following data;</u>
Acceleration = 0.500m/s²
a. To find the velocity of the boat after it has traveled 4.75 m
Since it started from rest, initial velocity is equal to 0m/s.
Now, we would use the third equation of motion to find the final velocity.
Where;
- V represents the final velocity measured in meter per seconds.
- U represents the initial velocity measured in meter per seconds.
- a represents acceleration measured in meters per seconds square.
- S represents the displacement measured in meters.
Substituting into the equation, we have;
Taking the square root, we have;
<em>Final velocity, V = 2.179 m/s.</em>
b. To find the velocity if the boat has traveled 50 m.
Taking the square root, we have;
<em>Final velocity, V = 7.071 m/s.</em>
Answer:
The force of car 3 on car 2 ≈ 1810.82 N
Explanation:
The equation for the change in momentum of the two cars are;
Conservation of linear momentum
150( 2.2 - v) = 265(1.5-v)
150 × 2.2 - 265×1.5 = (150+265)v
150 × 2.2 - 265×1.5 = -67.5 = 415×v
∴ v = -67.5/415 = -0.1627 m/s West = 0.1627 m/s East
The impulse of the net force is the amount of momentum change experienced given by the equation;
Impulse force = 
- 
Where;
= The final velocity
= The initial velocity
For the the 265 kg mass, we have;
= 0.1627 m/s
= 1.5 m/s
Which gives the impulse a s F×Δt = 265×0.1627 - 265×1.5 = -354.38 kg·m/s
The change in kinetic energy of the collision = 1/2×265×(0.1627^2 - 1.5^2) =-294.62 J
Whereby the distance moved in one second is 0.1627 m, we have;
Work done = Force × Distance = Force × 0.1627 = 294.62
Force = 294.62/0.1627 = 1810.82 N.
When the object is at the top of the hill it has the most potential energy. If it is sitting still, it has no kinetic energy. As the object begins to roll down the hill, it loses potential energy, but gains kinetic energy. The potential energy of the position of the object at the top of the hill is getting converted into kinetic energy. Hope this helped. :)
