The angle of refraction is 
Explanation:
Refraction is a wave phenomenon that occurs when a light wave passes through the interface between two mediums. When this occurs, the speed and the direction of the light wave change.
We can find the final direction of the refracted light in this problem by applying Snell's law:
where
are the index of refraction in the first and second medium, respectively
are the angle of incidence and refraction, respectively
In this problem, we have:
(the first medium is air, which has a refractive index of 1.00)
(index of refraction of crown glass)
is the angle of incidence
Solving for 
, we find the angle of refraction
Learn more about refraction and other wave phenomena:
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Explanation :
Work is done when a force is applied to create a displacement on an object.
Thus, the work done depends on the two factors i.e.
(1) Applied force (F)
(2) Distance or displacement (d)
Mathematically, work done is 
It also depends on the angle between the force and the displacement.
For example,
A person carries a weight of 20 kg and lifts it on his head 1.5 m above the surface. So, the work done by him on the luggage will be:
or
So, 
Hence, the work done by him on the luggage is 294 Joules.
part a)
Vector a has magnitude 12.3 and its direction is west, while Vector b has unknown magnitude and its direction is north. This means that the two vectors form a right-angle triangle, so a and b are two sides, while a+b is the hypothenuse.
We know the magnitude of a+b, which is 14.5, so we can use the Pythagorean theorem to calculate the magnitude of b:
part b) The direction of the vector a+b relative to west can be found by calculating the tangent of the angle of the right-angle triangle described in the previous part; the tangent of the angle is equal to the ratio between the opposite side (b) and the adjacent side (a):
And the angle is
with direction north-west.
part c)
This is exactly the same problem as the one we solved in part a): the only difference here is that the hypothenuse of the triangle is now given by a-b rather than a+b. In order to find a-b, we have to reverse the direction of b, which now points south. However, the calculations to get the magnitude of b are exactly the same as before, since the magnitude of (a-b) is the same as (a+b) (14.5 units), therefore the magnitude of b is still 7.68 units.
part d)
Again, this part is equivalent to part b); the only difference is that b points now south instead of north, so the vector (a-b) has direction south-west instead of north-west as before. Since the magnitude of the vectors involved are the same as part b), we still get the same angle, 
, but this time the direction is south-west instead of north-west.
Answer:
Explanation:
The engine should create the same force
1) F = ma
F = M(½a)
therefore
ma = ½Ma
m = ½M
M = 2m
M = 2(0.8)
M = 1.6 kg
2) Unbalanced forces
a. Two people pulling on the same side of a wheelbarrow
c. Two people of opposite sides of a big tire. One pushes the tire and one pulls it with equal force
3) b. The force of friction on the object is different if it is stationary or not
