Calculus 2: A large boulder dislodged by the falling coyote in exercise 9

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Cal2isFun

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A large boulder dislodged by the falling coyote in exercise 9 falls for 3 seconds before landing on the coyote. How far in meters did the boulder fall? What was the velocity in m/s when it flattened the coyote?
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Hello guys, I hope you are doing well! I actually didn't have any issues solving this question. My only question is as follows:
I found the impact velocity to be 29.4 m/s. My professor said it was wrong because the velocity at impact should have been -29.4 m/s, not 29.4 m/s. I guess it is right because it is a downward velocity.

However, there is another question in that textbook that asked for the same thing, but for some reason the velocity at impact is positive (according to the textbook answer at the end of the textbook). That exercise is: "A diver drop from 30 feet above the water. What is the diver's velocity impact?". The answer, according to the text book is ~30mph, not ~-30mph.

Is there something I am missing? Why does one question entail a negative velocity while another not? In both of them the velocity is downward. :unsure:

Thank you!
 
It depends on what coordinate system has been defined! If distances are measured upward, then in each case the velocity is negative. (Actually, technically, the velocity is a vector, not a number; but that is evidently not in view.) The speed in each case is positive.

The difference (if not just a matter of laxity on the book's part) may be in the details of the context and/or the exact wording of each problem, which you haven't quoted. For example, since the problem you do quote doesn't specify a coordinate system, I think a positive answer could be acceptable, but your professor may be commenting on what you wrote in your work. I don't know. You could ask ...
 
Dr.Peterson said:
It depends on what coordinate system has been defined! If distances are measured upward, then in each case the velocity is negative. (Actually, technically, the velocity is a vector, not a number; but that is evidently not in view.) The speed in each case is positive.

The difference (if not just a matter of laxity on the book's part) may be in the details of the context and/or the exact wording of each problem, which you haven't quoted. For example, since the problem you do quote doesn't specify a coordinate system, I think a positive answer could be acceptable, but your professor may be commenting on what you wrote in your work. I don't know. You could ask ...
Click to expand...

Thank you so much. No coordinates are mentioned. I provided the questions as they are written in the textbook. I assume they both occur in quadrant 1. Other than that, I believe, as you said, that the textbook was a bit careless about the negative sign?
 
Cal2isFun said:
Thank you so much. No coordinates are mentioned. I provided the questions as they are written in the textbook. I assume they both occur in quadrant 1. Other than that, I believe, as you said, that the textbook was a bit careless about the negative sign?
Click to expand...
Others may have different opinions; and the context I mentioned, such as instructions for a set of exercises, or even conventions used in a chapter or your classroom, might change things. I don't think quadrants are relevant, as we are really talking about one-dimensional motion -- one coordinate, not two.

But ultimately, on one hand the textbook answer author can be called careless, or the teacher can be called picky. In my opinion, since the problems don't define what should be called positive, a better answer in each case would be "29.4 m/s downward". Answers to applied problems should always be in terms of the question, not of the variables used in solving them.
 
Cal2isFun said:
A large boulder dislodged by the falling coyote in exercise 9 falls for 3 seconds before landing on the coyote. How far in meters did the boulder fall? What was the velocity in m/s when it flattened the coyote?
-----
Hello guys, I hope you are doing well! I actually didn't have any issues solving this question. My only question is as follows:
I found the impact velocity to be 29.4 m/s. My professor said it was wrong because the velocity at impact should have been -29.4 m/s, not 29.4 m/s. I guess it is right because it is a downward velocity.

However, there is another question in that textbook that asked for the same thing, but for some reason the velocity at impact is positive (according to the textbook answer at the end of the textbook). That exercise is: "A diver drop from 30 feet above the water. What is the diver's velocity impact?". The answer, according to the text book is ~30mph, not ~-30mph.

Is there something I am missing? Why does one question entail a negative velocity while another not? In both of them the velocity is downward. :unsure:

Thank you!
Click to expand...
Is this a question from Dynamics class or Calculus class?
 
Since this starts "A large boulder dislodged by the falling coyote in exercise 9" you really should post exercise 9 in case there is information in it that is needed.

And, one reason we ask that people post what they have tried is so that we will have an idea what you have available to work with.

Subhotosh Kahn asked "Is this a question from Dynamics class or Calculus class?" because there are two distinctly different ways of approaching this problem. Again, if you had posted what you have done on this problem, and what you do understand, we might have an idea what method you want to use.

If this is for a Dynamics class (or a "Pre-Calculus" class) then you may have been given a formula for the height of the boulder as a function of time. If it is for a Calculus class then might be expected to derive that formula from the fact that the acceleration due to gravity, the second derivative of height, is a constant, -9.81 m/s^2.

Which is it?
 
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