Answer:
Explanation:
From the given information:
Distance 
Speed of the comet 
At distance 
where;
mass of the sun = 
To find the speed 
:
Using the formula:
![E_f = E_i + 0 \\ \\ K_f + U_f = K_i + U_i \\ \\ = \dfrac{1}{2}mV_f^2 + \dfrac{-GMm}{d^2} = \dfrac{1}{2}mV_i^2+ \dfrac{-GMm}{d_i} \\ \\ V_f = \sqrt{V_i^2 + 2 GM \Big [ \dfrac{1}{d_2}- \dfrac{1}{d_i}\Big ]}](https://tex.z-dn.net/?f=E_f%20%3D%20E_i%20%2B%200%20%5C%5C%20%5C%5C%20%20K_f%20%2B%20U_f%20%3D%20K_i%20%2B%20U_i%20%20%5C%5C%20%5C%5C%20%3D%20%5Cdfrac%7B1%7D%7B2%7DmV_f%5E2%20%2B%20%20%5Cdfrac%7B-GMm%7D%7Bd%5E2%7D%20%3D%20%20%5Cdfrac%7B1%7D%7B2%7DmV_i%5E2%2B%20%5Cdfrac%7B-GMm%7D%7Bd_i%7D%20%5C%5C%20%5C%5C%20V_f%20%3D%20%5Csqrt%7BV_i%5E2%20%2B%202%20GM%20%5CBig%20%5B%20%20%5Cdfrac%7B1%7D%7Bd_2%7D-%20%5Cdfrac%7B1%7D%7Bd_i%7D%5CBig%20%5D%7D)
![V_f = \sqrt{(9.1 \times 10^{4})^2 + 2 (6.67\times 10^{-11}) *(1.98 * 10^{30} ) \Big [ \dfrac{1}{6*10^{12}}- \dfrac{1}{4.8*10^{10}}\Big ]}](https://tex.z-dn.net/?f=V_f%20%3D%20%5Csqrt%7B%289.1%20%5Ctimes%2010%5E%7B4%7D%29%5E2%20%2B%202%20%286.67%5Ctimes%2010%5E%7B-11%7D%29%20%2A%281.98%20%2A%2010%5E%7B30%7D%20%29%20%5CBig%20%5B%20%20%5Cdfrac%7B1%7D%7B6%2A10%5E%7B12%7D%7D-%20%5Cdfrac%7B1%7D%7B4.8%2A10%5E%7B10%7D%7D%5CBig%20%5D%7D)
Answer:
a= 92. 13 m/s²
Explanation:
Given that
Amplitude ,A= 0.165 m
The maximum speed ,V(max) = 3.9 m/s
We know that maximum velocity in the SHM given as
V(max) = ω A
ω=Angular speed
A=Amplitude
ω=23.63 rad/s
The maximum acceleration given as
a = ω² A
a= (23.63)² x 0.165 m/s²
a= 92. 13 m/s²
Therefore the maximum magnitude of the acceleration will be 92. 13 m/s².
Dispersion angle = 0.3875 degrees.
Width at bottom of block = 0.09297 cm
Thickness of rainbow = 0.07038 cm
Snell's law provides the formula that describes the refraction of light. It is:
n1*sin(θ1) = n2*sin(θ2)
where
n1, n2 = indexes of refraction for the different mediums
θ1, θ2 = angle of incident rays as measured from the normal to the surface.
Solving for θ2, we get
n1*sin(θ1) = n2*sin(θ2)
n1*sin(θ1)/n2 = sin(θ2)
asin(n1*sin(θ1)/n2) = θ2
The index of refraction for air is 1.00029, So let's first calculate the angles of the red and violet rays.
Red:
asin(n1*sin(θ1)/n2) = θ2
asin(1.00029*sin(40.80)/1.641) = θ2
asin(1.00029*0.653420604/1.641) = θ2
asin(0.398299876) = θ2
23.47193844 = θ2
Violet:
asin(n1*sin(θ1)/n2) = θ2
asin(1.00029*sin(40.80)/1.667) = θ2
asin(1.00029*0.653420604/1.667) = θ2
asin(0.39208764) = θ2
23.08446098 = θ2
So the dispersion angle is:
23.47193844 - 23.08446098 = 0.38747746 degrees.
Now to determine the width of the beam at the bottom of the glass block, we need to calculate the difference in the length of the opposite side of two right triangles. Both triangles will have a height of 11.6 cm and one of them will have an angle of 23.47193844 degrees, while the other will have an angle of 23.08446098 degrees. The idea trig function to use will be tangent, where
tan(θ) = X/11.6
11.6*tan(θ) = X
So for Red:
11.6*tan(θ) = X
11.6*tan(23.47193844) = X
11.6*0.434230136 = X
5.037069579 = X
And violet:
11.6*tan(θ) = X
11.6*tan(23.08446098) = X
11.6*0.426215635 = X
4.944101361 = X
So the width as measured from the bottom of the block is: 5.037069579 cm - 4.944101361 cm = 0.092968218 cm
The actual width of the beam after it exits the flint glass block will be thinner. The beam will exit at an angle of 40.80 degrees and we need to calculate the length of the sides of a 40.80/49.20/90 right triangle. If you draw the beams, you'll realize that:
cos(θ) = X/0.092968218
0.092968218*cos(θ) = X
0.092968218*cos(40.80) = X
0.092968218*0.756995056 = X
0.070376481 = X
So the distance between the red and violet rays is 0.07038 cm.
Answer:
So airplane will be 1324.9453 m apart after 2.9 hour
Explanation:
So if we draw the vectors of a 2d graph we see that the difference in angles is = 83 - 44.3 = 
Distance traveled by first plane = 730×2.9 = 2117 m
And distance traveled by second plane = 590×2.9 = 1711 m
We represent these distances as two sides of the triangle, and the distance between the planes as the side opposing the angle 38.7.
Using the law of cosine, 
representing the distance between the planes, we see that:
d = 1324.9453 m
Answer:
Mantle and core
Explanation:
The Mantle and Core are the two components within Earth experiencing convection. In several ways the mantle is significant. The one outcome of convective current is the creation of the fresh oceanic lithosphere around OCEANIC RIDGES, formed by mantle upwelling. Core is indeed the planet's innermost layer.
