An earthquake causes a 3 kg book to fall from a shelf. If the book lands with
1 answer:
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Answer:
The building is 26.85m tall.
Explanation:
In order to solve this problem, we must start by drawing a diagram of the situation. (See attached picture).
We split the height of the building into three parts: , the height of the window and
In order to find each of those, we need to start by finding the velocities of the ball in points A and B. We will analyze the trajectory of the ball when bouncing back to the top of the building. Let's start by finding the velocity of the ball in A:
We can use the following formula to determine the velocity of the ball in part A:
which can be solved for
so we get:
and now we can substitute (remember the acceleration of gravity goes downward so we will consider it to be negative).
which yields:
once we got the velocity at point A, we can now find the velocity at point B. We can do so by using the following formula:
which can be solved for which yields:
so we can substitute values now:
Which yields:
Now that we have the velocities at A and B, we can use them to find the values of and
Let's start with
We can use the following formula to find it:
we know the final velocity of the rebound will be zero, so we can simplify our formula:
so we can substitute now:
which solves to:
Now we can proceed and find the value of
the value of can be found by using the following formula:
in this case our t will be half of the tie spent below the bottom of the window, so:
so now we can substitute all the values in the given formula:
which yields:
so now that we have all the values we need, we can go ahead and calculate the height of the building:
when substituting we get:
So the answer is:
h=26.85m
The building is 26.85m tall.
