Alan G. answered • 06/03/16
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Ritwika,
Assuming the motion is in the xy-plane, you can describe the trajectory of the projectile using the parametric equations:
x = (u cos θ)t
y = (u sin θ)t - .5gt2 (assuming the projectile starts at the origin, (0,0))
You can produce a vector function from these equations:
r(t) = xi + yj, where t is the time variable.
The velocity function is r′(t). The speed is |r′(t)|.
I will not provide any more help until YOU answer the following question: What is the formula for curvature of an object moving through the plane (or space). I must know how you were taught this in order to answer the remainder of your question in a helpful way. Your question was classified as a physics problem, but it may actually be just a vector calculus problem.
Please let me know soon.
Alan G.
Ritwika,
Really! Why would you be asked a question on your test without having been taught about curvature? That is very strange.
I suspect that you may have been asked a bad test question. What I will do is do a little research on this offline and post a reply soon (if I can find a simple explanation). Honestly, I do not see how you could understand how to do this if your teacher has never explained the idea of curvature.
Please stay tuned. And be patient. I will try my best to help you with this question.
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06/03/16
Alan G.
It doesn't look like the answer you are supposed to be getting is correct. May I ask, where did this question arise? Was it from a textbook or instructor-authored exam? Or was it a standardized test question?
When you tell me this, I would like also to know where you are attending school, the name of your teacher, and his contact information. There is something very wrong here.
You should not be made to suffer like this, especially in a first semester calculus-based physics class. Your instructor or the test writer should be told about this problem. I am assuming throughout all of this that you correctly posed this question and it contains no errors itself.
Please respond soon.
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06/03/16
Ritwika B.
It is a question from IITJEE book. My tutuor gave me. 12th standard question.
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06/03/16
Alan G.
Ritwika,
I am not familiar with that textbook. If my guess is correct, it looks like it may be an electrical engineering textbook, right?
There is not much I can do about its content other than tell you what I discovered when I tried to answer your question. In order to insure accuracy, I fed the problem to a computer algebra system (after appropriate coding), and was given the following answer:
(ds/dt)/κ = -u2 tan θ.
This looks completely different from what you told me the answer should be, and I am not sure what you can do other than mention it to someone who can look into it as an expert. I consider myself qualified to state that I think the answer you posted is not correct. I justify that by pointing out that I have 26 years of experience teaching college level math, including calculus, and have made frequent use of physics in such classes (physics and calculus work well together).
It is really not my place to criticize course materials, but it looks like there may be an error in the problem you posted. If you are able to show it to someone who can look into it properly, I strongly advise doing this. No matter how often a textbook gets edited or revised, there are always errors that crop up.
One last thing you can do is provide me with the complete textbook title, page and location of the problem. Perhaps I can contact the publisher and point out a possible error in the printing of the book.
I am sorry I could not be more helpful, but I am offering to do the best I can to ensure no other student is frustrated by such a question again. Please let me know if I can be of more help to you.
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06/04/16
Ritwika B.
06/03/16