Why did the professor say that the student's method is wrong?

Steven G

Steven G

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A hot air balloon is rising directly upwards from the base of a hill at a rate of 30 feet per second. The hill is at an angle of π/6 to the horizontal. A rabbit sitting next to the balloon is startled by its launch and runs up the hill at 30 feet per second. How quickly is the distance between the rabbit and the hot air balloon changing after ten seconds? Your answer should include all relevant units.

The way I told this student to do this problem was by using the law of cosines. This method did get the correct answer.

The student however found a much easier method by realizing that the triangle is equilateral. The answer to the problem was immediate at that point. This method seemed much better than my method, but ...

The problem is that the student's professor said that she couldn't use the fact that the triangle was equilateral? Why is that or is the professor wrong?
 
Steven G said:
A hot air balloon is rising directly upwards from the base of a hill at a rate of 30 feet per second. The hill is at an angle of π/6 to the horizontal. A rabbit sitting next to the balloon is startled by its launch and runs up the hill at 30 feet per second. How quickly is the distance between the rabbit and the hot air balloon changing after ten seconds? Your answer should include all relevant units.

The way I told this student to do this problem was by using the law of cosines. This method did get the correct answer.

The student however found a much easier method by realizing that the triangle is equilateral. The answer to the problem was immediate at that point. This method seemed much better than my method, but ...

The problem is that the student's professor said that she couldn't use the fact that the triangle was equilateral? Why is that or is the professor wrong?
Click to expand...
Is this a challenge question or are you looking for an answer? I would say that the equilateral triangle thing is inspired but the student should be able to show how to do the problem for a general angle. It's not that the equilateral triangle approach is wrong, just that it is not an application of the more general method. That's my guess, anyway.

-Dan
 
Steven G said:
A hot air balloon is rising directly upwards from the base of a hill at a rate of 30 feet per second. The hill is at an angle of π/6 to the horizontal. A rabbit sitting next to the balloon is startled by its launch and runs up the hill at 30 feet per second. How quickly is the distance between the rabbit and the hot air balloon changing after ten seconds? Your answer should include all relevant units.

The way I told this student to do this problem was by using the law of cosines. This method did get the correct answer.

The student however found a much easier method by realizing that the triangle is equilateral. The answer to the problem was immediate at that point. This method seemed much better than my method, but ...

The problem is that the student's professor said that she couldn't use the fact that the triangle was equilateral? Why is that or is the professor wrong?
Click to expand...
I say the professor is wrong. Tkhunny used to say that correct answers do not care how you find them.

I have, however, a caveat; it is not intuitively obvious that the relevant triangle is equilateral. In a math class, should that not be demonstrated?
 
JeffM said:
I say the professor is wrong. Tkhunny used to say that correct answers do not care how you find them.

I have, however, a caveat; it is not intuitively obvious that the relevant triangle is equilateral. In a math class, should that not be demonstrated?
Click to expand...
Jeff,
The student did prove that the triangle was equilateral and the proof was perfect.
Steve
 
topsquark said:
Is this a challenge question or are you looking for an answer? I would say that the equilateral triangle thing is inspired but the student should be able to show how to do the problem for a general angle. It's not that the equilateral triangle approach is wrong, just that it is not an application of the more general method. That's my guess, anyway.

-Dan
Click to expand...
Sure, knowing how to do this with a general problem is better. The question is whether or not using (after proving) the fact that the triangle is equilateral is a valid way of solving this problem?
 
Steven G said:
Sure, knowing how to do this with a general problem is better. The question is whether or not using (after proving) the fact that the triangle is equilateral is a valid way of solving this problem?
Click to expand...
Of course it would be valid. My question is what was the teacher testing for? The solution or the method? I slightly disagree with TKHunny on this... if you are in a class sometimes it does matter how you get the answer. (That doesn't mean the teacher should have taken points off, if that's what you mean.)

-Dan
 
topsquark said:
Of course it would be valid. My question is what was the teacher testing for? The solution or the method? I slightly disagree with TKHunny on this... if you are in a class sometimes it does matter how you get the answer. (That doesn't mean the teacher should have taken points off, if that's what you mean.)

-Dan
Click to expand...
It was a homework assignment for an online class. The professor told the student to try again and said that she couldn't use the fact that the triangle was equilateral. Of course, that report to me was from the student and not the teacher.
 
Steven G said:
The hill is at an angle of π/6 to the horizontal.
Click to expand...

Isn't this hill at an angle of \(\displaystyle \ \dfrac{\pi}{3} \ \ radians \ = \ \) 60 degrees to the horizontal?

. ../
../
/______.<---- 60 degrees
 
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