What constellation does the Sun appear in front of on April 2nd? (You may use a sky chart from the Heavens-Above.com website or
2 answers:
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Answer:
Linear and rotational Kinetic Energy + Gravitational potential energy
Explanation:
The ball rolls off a tall roof and starts falling.
Let us first consider the potential energy or more specifically gravitational potential energy (;
= mass of the ball,
= acceleration due to gravity,
= height of the roof). This energy comes because someone or something had to do work to take the ball to the top of the roof against the force of gravity. The potential energy is naturally maximum at the top and minimum when the ball finally reaches the ground.
Now, the ball starts to roll and falls off the roof. It shall continue rotating because of inertia (Newton's first law). This contributes to the rotational kinetic energy (;
=moment of inertia of the ball &
= angular velocity).
Finally comes the linear kinetic energy or simply, kinetic energy () which is caused due to the velocity
of the ball.
Answer: 17.68 s
Explanation:
This problem is a good example of Vertical motion, where the main equation for this situation is:
(1)
Where:
is the height of the ball when it hits the ground
is the initial height of the ball
is the initial velocity of the ball
is the time when the ball strikes the ground
is the acceleration due to gravity
Having this clear, let's find from (1):
(2)
Rewritting (2):
(3)
This is a quadratic equation (also called equation of the second degree) of the form , which can be solved with the following formula:
(4)
Where:
Substituting the known values:
(5)
Solving (5) we find the positive result is: