Please see attached document. It's legit, no virus.

This question comes from my Introduction to Engineering class, but the instructor said he pulled it from a physics textbook. The instructor is a Physics professor and I guess he thought it would be entertaining to give this question to class full of freshmen. Maybe other freshmen have the skills, but my math is weak. I took remedial math last semester and now I'm in college algebra.

Anyway, the professor did "half" of the problem for us in class. He filled up 2 whiteboards with runes, most of which are not given in the problem. I was copying what he wrote down but then stopped, just to try to figure out what the heck he was doing, but I was totally lost. I do not even understand the question. What is it asking for? Am I supposed to plug some of the equations into eachother and simplify or what?

I don't think he really expects anybody to get this right, but I want to try anyway. I just don't know where to start.

 

It takes some reading through to get at the question but when you get to the bottom of it, it is not that difficult.

There are only two parameters, g and h.

Imagine you drop a ball to the floor and in bounces off the floor to a height h.
Now imagine that beside the bouncing ball you have a table of height less that h.
Let us for the moment give the table a height equal to k.

The question asks to calculate the length of time that the ball appears above the table.

 

It takes some reading through to get at the question but when you get to the bottom of it, it is not that difficult.

There are only two parameters, g and h.

Imagine you drop a ball to the floor and in bounces off the floor to a height h.
Now imagine that beside the bouncing ball you have a table of height less that h.
Let us for the moment give the table a height equal to k.

The question asks to calculate the length of time that the ball appears above the table.

so would I be correct in saying that the answer is in the question? In the second to last sentence, it say \(\sqrt{1-B}\) and this is the answer? It seems that way, when I plug in different fractions for β, I get reasonable percentages that reflect "hang time"
For β = ½
70%
For β = ¾
50%
For β = ¼
86%

There are 3 values of β, but I seriously doubt that I have satisfied the requirement of the problem. As I said, the prof filled 2 white boards (not an exaggeration) and then said that he "had gotten us half way there." I have a feeling that \(\sqrt{1-B}\) is the answer, but the instructor is expecting us to show how this answer was derived from the formulas given.

 

Yes, the answer is in the question.
But you are required to show how that is the answer.

So you have to calculate the total time the ball is in the air (from floor to peak or peak to floor)
and the time the ball is above the table (from table to peak or peak to table).

He has given you three equations. You only need to use one of the three.

 

This is a classic physics problem:

You hold the ball above the ground it contains potential energy given by: mgh but it has zero kinteic energy since it's velocity is zero.

If you release it, the ball accelerates toward the floor and acquires kinetic energy in velocity. When it hits the floor all of it's potential energy has been transferred to kinetic energy.

Assuming a perfectly elastic collision with the floor (no energy loss) it rebounds and goes back up to the height it started from, again having all potential energy and zero kinetic energy.

 

Ok, He states that it's an algebra problem. The only way I know to approach the problem is to rearrange the given equations, plug them into eachother and simplify, in hopes that it boils down to \(\sqrt{1-\beta}\). Attached is the progress which I haven't made so far.

 

The time it takes for the ball to reach the floor is the same as the time it takes for the ball to bounce off the floor and reach its maximum height.

The only equation you need is:

\(y = vt - \frac{1}{2}gt^2\)

set \(v = 0\)

Calculate the time it takes to travel \(y\)

and the time it takes to travel \((1-\beta)y\)