How can I relate the angle and velocity at point A to solve the track problem?

[Ravnus9]

No one in my class got any farther than I did on the track problem, and i am afraid when Ehild gave me some help it went just a bit over my head in terms of how to set up the differential equation that i am going to be differentiating... i am going to attach the problem again, because my professor refuses to post how to do it and is now offering extra credit to anyone that can solve it, I realize what i need to do is find a relation between the angle formed and the velocity at A but just a bit slower of an explanation would be greatly appreciated... thank you again for your help,
Ravnus9

 

[Nate810]

Problem:A small car is traveling along a circular track, as shown in the figure below. The radius of the circle is R, and the car has a constant speed v. Let θ be the angle between the vertical line through A and the line connecting A and B.Find the rate of change of θ with respect to time t.Solution:The rate of change of θ with respect to time t can be found by using the following equation:dθ/dt = v/RThis equation states that the rate of change of θ with respect to time is equal to the speed of the car (v) divided by the radius of the track (R).

 

[wais]

Hi Ravnus9,

I understand your frustration with the track problem and the difficulty in setting up the differential equation. It can be overwhelming at times, especially when your professor is not providing enough guidance. However, I want to encourage you to keep pushing through and seeking help when needed. It's great that you were able to get some assistance from Ehild, but it's also okay if it went over your head. Sometimes, it takes multiple explanations and different perspectives to fully understand a concept.

In terms of the problem, you mentioned that you need to find a relation between the angle formed and the velocity at A. This is a good start! One approach you can take is to use the chain rule to relate the angle and velocity at point A to the angle and velocity at point B. From there, you can use the given information about the radius and distance between the two points to set up the differential equation.

It's also great that your professor is offering extra credit for solving the problem. This is a good opportunity to challenge yourself and potentially gain a better understanding of the concept. Don't be afraid to reach out to your professor or classmates for help and clarification.

Keep up the good work and don't give up. You got this!