This is an interesting (read tricky!) variation of Rydberg Eqn calculation.
Rydberg Eqn: 1/λ = R [1/n1^2 - 1/n2^2]
Where λ is the wavelength of the light; 1282.17 nm = 1282.17×10^-9 m
R is the Rydberg constant: R = 1.09737×10^7 m-1
n2 = 5 (emission)
Hence 1/(1282.17 ×10^-9) = 1.09737× 10^7 [1/n1^2 – 1/25^2]
Some rearranging and collecting up terms:
1 = (1282.17 ×10^-9) (1.09737× 10^7)[1/n2 -1/25]
1= 14.07[1/n^2 – 1/25]
1 =14.07/n^2 – (14.07/25)
14.07n^2 = 1 + 0.5628
n = √(14.07/1.5628) = 3
To solve this problem we will use the related concepts in Newtonian laws that describe the force of gravitational attraction. We will use the given value and then we will obtain the proportion of the new force depending on the Radius. From there we will observe how much the force of attraction increases in the new distance.
Planet gravitational force



Distance between planet and star

Gravitational force is

Applying the new distance,


Replacing with the previous force,

Replacing our values


Therefore the magnitude of the force on the star due to the planet is 
The concept to develop this problem is the Law of Malus. Which describes what happens with the light intensity once it passes through a polarized material.
Mathematically this can be expressed as

Where
I = New intensity after pass through the Polarizer
= Original intensity
= Indicates the angle between the axis of the analyzer and the polarization axis of the incident light.
When the light passes perpendicularly through the first polarizer, the light intensity is reduced by half which will cause the intensity to be
at the output of the new polarizer, mathematically:


Solving to find the angle we have

The orientation angle of the second polarizer relative to the first one is 43.11°
The car’s momentum after 4.21s is 24617.4 kgm/s
<h3>
Newton's Second Law of Motion.</h3>
Newton's second law state that, the rate of change of momentum, is directly proportional to the applied force.
Given that a 1200 kg car passes traffic light at a velocity of 10.2 m/s to the north and accelerates at a rate of 2.45 m/s^2. To calculate the car’s momentum after 4.21 s, Let us first list all the parameters involved.
- Acceleration a = 2.45 m/s²
From Newton's second law,
F = (mv - mu) / t
ma = (mv - mu) / t
Substitute all the parameters into the formula above.
1200 × 2.45 = ( mv - 1200 × 10.2 ) / 4.21
2940 = ( mv - 12240 ) / 4.21
Cross multiply
12377.4 = mv - 12240
Make mv the subject of the formula
mv = 12377.4 + 12240
mv = 24617.4 kgm/s
Therefore, the car’s momentum after 4.21s is 24617.4 kgm/s
Learn more about Momentum here: brainly.com/question/25121535
#SPJ1