# Calculating average speed.

My problem states, that a ball is thrown from the top of a building. At the same instance a person is running on the ground at a distance of 32.6 m away from the building. I have to find the average speed the runner must be traveling to catch the ball at the bottom of the building.

So far I have calculated everything related to the ball. As in how long it was in the air, it's velocity, and it's maximum height. All calculations I believe are correct.

Now, however, I'm stuck in that I don't know what to do next. I know I need to find the average speed the runner must be going. So I'm assuming that the velocity of the ball and the time the ball is in the air will play a factor in this. I'm just stuck I don't know where to go from here.

Doc Al
Mentor
Realize that the runner better make it to the building (travel 32.6 m) in exactly the time it takes for the ball to hit the ground. You have the distance; you have the time. Find the speed.

Just to clarify, time is how long the ball is in the air, correct? So I need to find velocity, and I have distance, and time. Don't I need a third variable to find the velocity?

Doc Al
Mentor
BlackMamba said:
Just to clarify, time is how long the ball is in the air, correct?
Right.
So I need to find velocity, and I have distance, and time. Don't I need a third variable to find the velocity?
V = D/T.

Of course. Maybe next time I should just look it up instead of asking a million silly questions.

Well I must have done something wrong finding the time. Because with everything that I did, I still don't have the right answer.

Here's the problem word for word and my work that I did:

A ball is thrown upward from the top of a 24.8m tall building. The ball's initial speed is 12 m/s. At the same instant, a person is running on the ground at a distance of 32.6m from the building. What must be the average speed of the person if he is to catch the ball at the bottom of the building.?

So to find time I used the equation: T = V - Vo/A And found T to be 1.22 s. I'm thinking now that I did this part wrong.

Ok well I realized that I didn't double my T answer and thought that solved the problem, but it did not.

Doc Al
Mentor
finding the time

BlackMamba said:
Well I must have done something wrong finding the time. Because with everything that I did, I still don't have the right answer.
Use this kinematic equation for position as a function of time:
$$y = y_0 + v_0 t + 1/2 a t^2$$
$y_0 = 24.8 m$
$y = 0 m$
$v_0 = 12 m/s$
$a = -9.8 m/s^2$
Solve the equation for t.

Forgive me here but how do I get t alone? Since there is VoT and then 1/2AT^2.

Doc Al
Mentor
Time for you to get familiar with quadratic equations!

I suppose it is. LOL

Ok so I've been trying like a good student should. LOL This is what I've gotten so far. I believe this is my quadratic equation: 0 = 24.8 + 12t - 4.9t^2

Still I have no idea how to solve for just t? There has to be an easier way to do this.

Gokul43201
Staff Emeritus
Gold Member
No, there isn't. That's a simple quadratic aquation of the form : Ax^2 + Bx + C = 0.

What are the solutions of such a quadratic ? x = ....... ?

Gokul43201
Staff Emeritus
Gold Member
Actually, there is another way to do this problem that avoids the need to solve the above type of quadratic equation. I'm not going to say what that is, since it would do you a whole lot of good to learn the solution to quadratic equations - it's not hard at all, and will serve you well in the future.

Apparently, I'm just not supposed to get this one right. I found time using the quadratic equation. Well at least I think I did. However each answer was positive. So I tried to find the velocity using either answer and both were wrong. What is my problem here?

My quadratic equation was : 0 = 24.8 + 12t - 4.9t^2

So in solving for t my answers were 0.62 if I added the top two numbers and 1.83 if I subtracted the top numbers. However then when I tried to find the velocity with either number I had no luck. Where am I going wrong?

Doc Al
Mentor
BlackMamba said:
Apparently, I'm just not supposed to get this one right. I found time using the quadratic equation. Well at least I think I did. However each answer was positive. So I tried to find the velocity using either answer and both were wrong. What is my problem here?
My quadratic equation was : 0 = 24.8 + 12t - 4.9t^2
Right.
So in solving for t my answers were 0.62 if I added the top two numbers and 1.83 if I subtracted the top numbers. However then when I tried to find the velocity with either number I had no luck. Where am I going wrong?
I've no idea what you mean by "added the top two numbers". I suspect you are just trying things at random! :grumpy: Don't do that: Solve the quadratic properly!

Integral
Staff Emeritus
Gold Member
If you told us how you arrived at the numbers you give we may be able tell you what you did wrong.

Those are not the numbers I get as roots to the equation you give.

I'm not just trying things at random. Contrary to what I might be saying, I actually do need to learn something from this class. I knew what I said was quite vague, but since EVERYONE knows how to do quadratic equations, I naturally assumed that someone would understand. Give me a minute to properly show you my work without it being all jumbled.

OK. So I must be as dumb as I am protraying myself on here. As I was preparing my work to show you, I noticed that I forgot a negative sign.

In saying that, I found t to be 3.79. Would I be correct on this?

Doc Al
Mentor
Yes. Much better.

I decided to post my work anyway just to show that I am seriously doing this work. :)

Thank you everyone for your help. It truely is greatly appreciated.

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