Answer:
This is because The energies of atoms are quantized.
Electrons are allowed "in between" quantized energy levels, and, thus, only specific lines are observed
Answer:
The angular velocity is 15.37 rad/s
Solution:
As per the question:

Horizontal distance, x = 30.1 m
Distance of the ball from the rotation axis is its radius, R = 1.15 m
Now,
To calculate the angular velocity:
Linear velocity, v = 
v = 
v = 
v = 
Now,
The angular velocity can be calculated as:

Thus

Velocity is the rate of change of position with respect to time, whereas acceleration is the rate of change of velocity. Both are vector quantities (and so also have a specified direction), but the units of velocity are meters per second while the units of acceleration are meters per second squared.
maximum speed of cheetah is

speed of gazelle is given as

Now the relative speed of Cheetah with respect to Gazelle


now the relative distance between Cheetah and Gazelle is given initially as "d"
now the time taken by Cheetah to catch the Gazelle is given as

so by rearranging the terms we can say


so above is the relation between all given variable