Problem with Classic where do they meet Problem

[derekfuselier]

Problem with Classic "where do they meet" Problem

I have always had problems with these types of concepts because no one has ever showed me exactly what is required to solve the problem. Anyways, here it is:

In an historical movie, two knights on horseback start from rest 99.8 m apart and ride directly toward each other to do battle. Sir George's acceleration has a magnitude of 0.207 m/s^2, while Sir Alfred's has a magnitude of 0.229 m/s^2. Relative to Sir George's starting point, where do the knights collide?

I was instructed to, using the kinematic equation Xf = Xi + (Vi)(t) + (1/2)(a)(t)^2, find t^2 and sub into the other equation, but doing that leaves me with a variable, x, on each side of the equation. Any help would be extremely appreciated, thanks!

 

[cristo]

How did you set up your equations? Take George to start at point x=0, and Arthur to start at point x=99.8, and use the equation you have written (one for each horse). Now, when the knights meet, what can you say about the displacements of the two knights? Can you calculate t from this? If so, then you should be able to find x.

Show your working, and we will be able to help!

 

[Panda]

Can you show how you substituted?

What values were you using for? e.g.
Knight1 - Xi, Vi, a
Knight2 - Xi, Vi, a

 

[derekfuselier]

Sorry guys, let me draw it up and scan then I'll show my work. Thanks so much!

 

[derekfuselier]

Ok, my work is attached.

 

[derekfuselier]

How did you set up your equations? Take George to start at point x=0, and Arthur to start at point x=99.8, and use the equation you have written (one for each horse). Now, when the knights meet, what can you say about the displacements of the two knights? Can you calculate t from this? If so, then you should be able to find x.

Show your working, and we will be able to help!

Well George would be displaced by x and Albert by 99.8 - x, right? If not, blame the Louisiana schools ;)

 

[cristo]

Albert will be displaced from his starting point by 99.8-x, but the question asks for the displacement of him relative to george's starting point

So, you need to set up a coordinate system with origin on george's starting point. Thus, relative to this coordinate system, what are the accelerations of each knight?

(I can't see your attachment yet; it needs to be approved, but I'll try and hurry the process up!)

 

[derekfuselier]

Albert will be displaced from his starting point by 99.8-x, but the question asks for the displacement of him relative to george's starting point

So, you need to set up a coordinate system with origin on george's starting point. Thus, relative to this coordinate system, what are the accelerations of each knight?

(I can't see your attachment yet; it needs to be approved, but I'll try and hurry the process up!)

I understand that they are asking for distance relative to George's position. However, I'm not quite sure what you mean by this coordinate system.

 

[cristo]

Ok, I've seen your work now. (I like your pictures of horses!) I've not checked your arithmetic, but youv'e made a mistake in calculating t.

Note that, you have two equations for x_f, so set them equal to each other and you will get an expression \frac{1}{2}0.207t^2=99.8-\frac{0.229}{2}t^2 (1)

Solve this for t, and then sub into one of the equations to obtain x_f

(Sorry, the first time I glanced through and didn't pick this up. I only noticed when I calculated x_f from your last equation and it turned out to be >99.8. So, if you read my first response, I apologise as my commenets were not correct!)

edit:

I understand that they are asking for distance relative to George's position. However, I'm not quite sure what you mean by this coordinate system.

Ignore that; I was just hinting at the fact that one acceleration is negative, but after looking at your work, I can see that you know this!

 

[derekfuselier]

Maybe I just can't see how to solve for t because I've been working problems for too long or I could just be an idiot.

 

[cristo]

Maybe I just can't see how to solve for t because I've been working problems for too long or I could just be an idiot.

Id go for the former reason! In my equation (1) in my last post, simplify it by putting all the terms involving t² onto one side. Then you'll have an expression At²=99.8, where A is a number. Divide both sides by A, take the square root, and you will obtain the value of t.

Then, sub this into one of the equations for x_f in your work, and you will obtain x_f

 

[derekfuselier]

Id go for the former reason! In my equation (1) in my last post, simplify it by putting all the terms involving t² onto one side. Then you'll have an expression At²=99.8, where A is a number. Divide both sides by A, take the square root, and you will obtain the value of t.

Then, sub this into one of the equations for x_f in your work, and you will obtain x_f

Lol, thanks! But I still don't see how to put them on the same side To me, algebraically, to get them on the same side on must divide by t^2 which would cancel out the other t^2. I'm feeling especially dense right now.

Lol, oh my. Subtract, factor out, etc..what's wrong with me? Thanks!