Calculus - Derivative question

[apchemstudent]

The top of a 25 feet ladder is sliding down a wall at a constant rate of 3 ft/min. What is the rate of change in distance between the bottom of the ladder and the wall, when the top of the ladder from the ground is 7ft?

I got the answer as 7/8 ft /min. However, my teacher says
the answer is -7/8 ft/min. This doesn't make any sense since the distance between the bottom of the ladder and the wall is definitely increasing, not decreasing and yet the answer is negative.

So which one is the correct answer? please help. thanks...

 

[mjfairch]

Issues like this depend on the coordinate system imposed. Assume a right-handed coordinate system where the origin is located at the point where the wall and floor meet. Let the positive y-axis run directly up the wall and the positive x-axis run along the ground toward the right. Now, if the ladder is sliding out to the LEFT, then with our coordinate system it will have a negative velocity, but if it is sliding to the right, then it will have a positive velocity. The sign just depends on the coordinate system superimposed over the physical situation.

Cheers.
---
Mike Fairchild
http://www.mikef.org/
"Euclid alone has looked on beauty bare."
--Edna St. Vincent Mallay

 

[NeutronStar]

What is the rate of change in distance between the bottom of the ladder and the wall, when the top of the ladder from the ground is 7ft?

Based on the question as worded above I would agree that the rate is positive. I wouldn't worry too much about it. The sign of a rate is almost always dependent on the point of view. Sometimes you have to miss points because of personality clashes rather than because of mathematical errors.

He also might have been thinking in terms of the distance between the top of the ladder and the floor which would be negative. But that isn't what the question asked. I'd take a point off the professor's Ph.D. if it were me.

I had a physics professor once who swore up and down that the time dilation of the twin-brother paradox has nothing to do with acceleration. Yeah right.

Sometimes you just have to bite the bullet for losing points even though you know you're right!

 

[ComputerGeek]

The top of a 25 feet ladder is sliding down a wall at a constant rate of 3 ft/min. What is the rate of change in distance between the bottom of the ladder and the wall, when the top of the ladder from the ground is 7ft?

I got the answer as 7/8 ft /min. However, my teacher says
the answer is -7/8 ft/min. This doesn't make any sense since the distance between the bottom of the ladder and the wall is definitely increasing, not decreasing and yet the answer is negative.

So which one is the correct answer? please help. thanks...

your teacher should not be so anal. Frame of reference can cause shifts in the direction of the motion like that, but neither is more correct over the other unless it is used in a context of another measurement. in that case you want your frames of reference to match.

 

[ComputerGeek]

I had a physics professor once who swore up and down that the time dilation of the twin-brother paradox has nothing to do with acceleration. Yeah right.

Is that a joke? He must have been one of those old profs who had a lot of pride and did not like to be contradicted even when wrong.

 

[derekmohammed]

Personally I don't think it is anal to want to set up a convention properly. Without convention nothing on this Earth would work properly! Everyone would be confused because there would be no set order. The best thing you can do as a student is try to agree with your teachers when it comes to silly things like convention! It makes likfe a lot easier when you do encounter REAL anal proffesers!

 

[NeutronStar]

Is that a joke? He must have been one of those old profs who had a lot of pride and did not like to be contradicted even when wrong.

No, it wasn't a joke. And she was not very old at 40. She was actually quite bright and her main interest was with astronomy. I'm not sure why she didn't get the connection between acceleration and time dilation. She kept trying to tell me that time dilation has to do with Special Relativity which doesn't address acceleration. She said that General Relativity addresses acceleration and time dilation is definitely a Special Relativity topic so accleration is unimportant for time dilation.

I was trying to explain to her that even in Special Relativity acceleration is important because it's the only way to get from one inertial frame to another. She did agree with that, but still insisted that acceleration is unimportant for time dilation.

Well, she might be technically correct in the long run because time dilation does not require acceleration to maintain it, but we were actually discussing the twin brother's paradox. And in that situation at least one of the two twins would need to undergo an acceleration. My point was that the one that undergoes the acceleration will be the younger twin when they get back together. She disagreed with me and maintained that it was only their relative speeds that caused the time dilation, then she refused to discuss it anymore.

Personally I think she was confused about the whole thing and wasn't about to admit that to a student. She certainly wasn't about to permit me to explain it to her. Maybe she was just having a bad-hair day.

 

[HallsofIvy]

It's seldom a good idea to argue with a professor but some might be willing to give a "detailed explanation" of their answer if asked for it. I would like to see WHY the professor thinks the answer is negative. It is NOT a question of coordinate systems because the problem asked for the rate of change of DISTANCE.

 

[ComputerGeek]

well, sure, Time dilation can occur in the presence of gravity, but in that case you are still talking about acceleration :-)

 

[ComputerGeek]

It's seldom a good idea to argue with a professor but some might be willing to give a "detailed explanation" of their answer if asked for it. I would like to see WHY the professor thinks the answer is negative. It is NOT a question of coordinate systems because the problem asked for the rate of change of DISTANCE.

I see where you are going with that. since one is speaking only of distance, then you are dealing with a case of magnitude and no direction. that would be a good argument for full credit "The question asked for Distance, not Displacement sir".

though one might want to argue that after class so as not to risk the prof feeling silly and getting angry about it :-)

 

[mjfairch]

we were actually discussing the twin brother's paradox. And in that situation at least one of the two twins would need to undergo an acceleration. My point was that the one that undergoes the acceleration will be the younger twin when they get back together. She disagreed with me and maintained that it was only their relative speeds that caused the time dilation, then she refused to discuss it anymore.

You may want to refer to the following URL for a semi-detailed discussion on a variation of this "paradox." This discussion demonstrates the importance of the relativity of simultaneity in resolving the twin "paradox" (falsely so called):

http://bcs.whfreeman.com/tiplermodernphysics4e/content/cat_020/IdenticallyAcceleratedTwins.pdf

This is from the book, Modern Physics, 4/E by Tipler and Llewellyn.

Cheers.
---
Mike Fairchild
http://www.mikef.org/
"Euclid alone has looked on beauty bare."
--Edna St. Vincent Mallay