Answer:
Distance will be ![=3960\times 0.12385=490.468miles](https://tex.z-dn.net/?f=%3D3960%5Ctimes%200.12385%3D490.468miles)
Explanation:
We have given that Buffalo has a latitude of 42.9°N
And Raleigh has a latitude of 35.8°N
Radius of the earth = 3960 miles
We have to calculate the distance between given two cities
Difference in their latitudes = ![42.9-35.8=7.1^{\circ}](https://tex.z-dn.net/?f=42.9-35.8%3D7.1%5E%7B%5Ccirc%7D)
Now changing the angle in radian = ![7.1\times\frac{\pi }{180}=0.12385radian](https://tex.z-dn.net/?f=7.1%5Ctimes%5Cfrac%7B%5Cpi%20%7D%7B180%7D%3D0.12385radian)
So distance will be ![=3960\times 0.12385=490.468miles](https://tex.z-dn.net/?f=%3D3960%5Ctimes%200.12385%3D490.468miles)
The solution is 22 2(n+3)-4&6
Answer:
The first part can be solved via conservation of energy.
![mgh = mg2R + K\\K = mg(h-2R)](https://tex.z-dn.net/?f=mgh%20%3D%20mg2R%20%2B%20K%5C%5CK%20%3D%20mg%28h-2R%29)
For the second part,
the free body diagram of the car should be as follows:
- weight in the downwards direction
- normal force of the track to the car in the downwards direction
The total force should be equal to the centripetal force by Newton's Second Law.
![F = ma = \frac{mv^2}{R}\\mg + N = \frac{mv^2}{R}](https://tex.z-dn.net/?f=F%20%3D%20ma%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D%5C%5Cmg%20%2B%20N%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D)
where
because we are looking for the case where the car loses contact.
![mg = \frac{mv^2}{R}\\v^2 = gR\\v = \sqrt{gR}](https://tex.z-dn.net/?f=mg%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D%5C%5Cv%5E2%20%3D%20gR%5C%5Cv%20%3D%20%5Csqrt%7BgR%7D)
Now we know the minimum velocity that the car should have. Using the energy conservation found in the first part, we can calculate the minimum height.
![mgh = mg2R + \frac{1}{2}mv^2\\mgh = mg2R + \frac{1}{2}m(gR)\\gh = g2R + \frac{1}{2}gR\\h = 2R + \frac{R}{2}\\h = \frac{5R}{2}](https://tex.z-dn.net/?f=mgh%20%3D%20mg2R%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%5C%5Cmgh%20%3D%20mg2R%20%2B%20%5Cfrac%7B1%7D%7B2%7Dm%28gR%29%5C%5Cgh%20%3D%20g2R%20%2B%20%5Cfrac%7B1%7D%7B2%7DgR%5C%5Ch%20%3D%202R%20%2B%20%5Cfrac%7BR%7D%7B2%7D%5C%5Ch%20%3D%20%5Cfrac%7B5R%7D%7B2%7D)
Explanation:
The point that might confuse you in this question is the direction of the normal force at the top of the loop.
We usually use the normal force opposite to the weight. However, normal force is the force that the road exerts on us. Imagine that the car goes through the loop very very fast. Its tires will feel a great amount of normal force, if its velocity is quite high. By the same logic, if its velocity is too low, it might not feel a normal force at all, which means losing contact with the track.
radiation
when the suns radiation fall on the earth and its objects they receive heat energy and hence get heated. Thus the suns heat reaches the earth by. the process of radiation