Answer:
14 rev
Explanation:
= initial angular velocity = 2.5 revs⁻¹
= final angular velocity = 0.8 revs⁻¹
= Angular acceleration = - 0.2 revs⁻²
= Angular displacement
Using the equation

So the number of revolutions are 14
Answer:
106.7 N
Explanation:
We can solve the problem by using the impulse theorem, which states that the product between the average force applied and the duration of the collision is equal to the change in momentum of the object:

where
F is the average force
is the duration of the collision
m is the mass of the ball
v is the final velocity
u is the initial velocity
In this problem:
m = 0.200 kg
u = 20.0 m/s
v = -12.0 m/s

Solving for F,

And since we are interested in the magnitude only,
F = 106.7 N
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A) The resultant force is 30.4 N at 
B) The resultant force is 18.7 N at 
Explanation:
A)
In order to find the resultant of the two forces, we must resolve each force along the x- and y- direction, and then add the components along each direction to find the components of the resultant.
The two forces are:
at
above x-axis
at
above y-axis
Resolving each force:


So, the components of the resultant are:

And the magnitude of the resultant is:

And the direction is:

B)
In this case, the 15 N is applied in the opposite direction to the 20 N force. Therefore we need to re-calculate its components, keeping in mind that the angle of the 15 N force this time is

So we have:

So, the components of the resultant this time are:

And the magnitude is:

And the direction is:

Learn more about vector addition:
brainly.com/question/4945130
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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