The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:
(1)
where m is the sister's mass, g is the gravitational acceleration and
is the increase in altitude of the sister with respect to its initial position.
By calling
the angle of the chain with respect to the vertical, the increase in altitude is given by
(2)
where L is the length of the chain.
Putting (2) inside (1), we find
from which we can find the mass of the sister:
If you count the number of seconds between the flash of lightning and the sound of thunder, and then divide by 5, you'll get the distance in miles to the lightning: 5 seconds = 1 mile, 15 seconds = 3 miles, 0 seconds = very close. Keep in mind that you should be in a safe place while counting.
The answer is C. I hope I helped!
Answer:
The angular velocity is 
Explanation:
From the question we are told that
The mass of each astronauts is 
The initial distance between the two astronauts 
Generally the radius is mathematically represented as 
The initial angular velocity is 
The distance between the two astronauts after the rope is pulled is 
Generally the radius is mathematically represented as 
Generally from the law of angular momentum conservation we have that
Here 
is the initial moment of inertia of the first astronauts which is equal to 
the initial moment of inertia of the second astronauts So
Also 
is the initial angular velocity of the first astronauts which is equal to 
the initial angular velocity of the second astronauts So
Here 
is the final moment of inertia of the first astronauts which is equal to 
the final moment of inertia of the second astronauts So
Also 
is the final angular velocity of the first astronauts which is equal to 
the final angular velocity of the second astronauts So
So
=> 
=> 
=> 
=>
This is due to the tilt of the earth on its axis. Although the Sun shines on Earth, because of how the Earth is tilted, the equator is more directly hit compared to places found on the poles. The poles are hit at an angle, therefore the sunlight they receive is lesser than the places at the equator.
