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Answer:
Explanation:
The average velocity is total displacement divided by time:
And in the case of vertical
where is the total vertical displacement of the rock.
The vertical displacement of the rock when it is thrown straight up from height with initial velocity
is given by:
The time it takes for the rock to reach maximum height is when , and it is
The vertical distance it would have traveled in that time is
This is the maximum height the rock reaches, and after it has reached this height the rock the starts moving downwards and eventually reaches the ground. The distance it would have traveled then would be:
Therefore, the total displacement throughout the rock's journey is
Now wee need to figure out the time of the journey.
We already know that the rock reaches the maximum height at
and it should take the rock the same amount of time to return to the roof, and it takes another to go from the roof of the building to the ground; therefore,
where is the time it takes the rock to go from the roof of the building to the ground, and it is given by
we solve for using the quadratic formula and take the positive value to get:
Therefore the total time is
Now the average velocity is