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bobobob111

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There are 2 cars, a black car and a blue car, involved in a race. The black car is racing on a track that is circular and has a radius of 100ft while the blue car is racing on a track that is linear (straight line). The linear one is tangent to the circle track. Say the two cars start from the point of tangency and have identical starts in the same direction travelling 10ft/s. We are wondering how fast the angle between the two cars, from the perspective of someone from the circular track, will be changing when the black car is one-eight of the way around the circle.

For my answer I got 45degrees/7.85seconds= 5.73 deg/sec. I got that by taking 1/8th of the track is 78.5ft. Then i divided that by 10ft/s to get how long it would take to go that distance. I'm not sure this is the correct way of doing this because I'm supposed to be using calculus and I'm not sure how to incorporate that. Any help is much appreciated!
 
When you say, "the angle between the two cars, from the perspective of someone from the circular track", do you mean someone at the starting point (A, below)? If so, then calculus isn't required, because there is a simple relationship between that angle (between the tangent and a chord) and the central angle (at O below), which is changing at a constant rate.

1592920670656.png

But you haven't used that relationship; you seem to be thinking only of the central angle, which has nothing to do with where the blue car is.

If you want to use calculus, then write an equation for the angle you are interested in as a function of time, or of the position of the car, or whatever you like. Then differentiate. (You could use an equation based on the angle relationship I've alluded to.)
 
I really am not sure. It directly says " calculate the angle between them as viewed from the circle." So, I'm guessing it's talking about angle A? If so I'm a bit confused as to do I should do.
 
Please state the entire problem exactly as given to you, ideally as an image. If it is as you say, then we have to guess what it means! There are infinitely many places on the circle.

Also, do you know the relationship I referred to, from a geometry class? Or would you like to use trigonometry and coordinate geometry? There are many ways to approach this.
 
There are 2 cars, a black car and a blue car, involved in a race. The black car is racing on a track that is circular and has a radius of 100ft while the blue car is racing on a track that is linear (straight line). The linear one is tangent to the circle track. Say the two cars start from the point of tangency and have identical starts in the same direction travelling 10ft/s. We are wondering how fast will the angle between the two cars, as viewed from the circle, be changing when the black car is one-eight of the way around the circle. That is the exact wording. I'm not exactly sure of the relationship you are talking about. Do you mean the fact that the angle is 90 degrees between tangent and chord?
 
bobobob111 said:
There are 2 cars, a black car and a blue car, involved in a race. The black car is racing on a track that is circular and has a radius of 100ft while the blue car is racing on a track that is linear (straight line). The linear one is tangent to the circle track. Say the two cars start from the point of tangency and have identical starts in the same direction travelling 10ft/s. We are wondering how fast will the angle between the two cars, as viewed from the circle, be changing when the black car is one-eight of the way around the circle. That is the exact wording. I'm not exactly sure of the relationship you are talking about. Do you mean the fact that the angle is 90 degrees between tangent and chord?
Click to expand...
You say:

There are 2 cars, a black car and a blue car, involved in a race. The black car is racing on a track that is circular and has a radius of 100ft while the blue car is racing on a track that is linear (straight line). The linear one is tangent to the circle track. Say the two cars start from the point of tangency and have identical starts in the same direction travelling 10ft/s. We are wondering how fast will the angle between the two cars, as viewed from the circle, be changing when the black car is one-eight of the way around the circle.

That is the exact wording.
Click to expand...
The statement does not "read" like a formal statement. Please post a photocopy of your problem statement.
 
bobobob111 said:
There are 2 cars, a black car and a blue car, involved in a race. The black car is racing on a track that is circular and has a radius of 100ft while the blue car is racing on a track that is linear (straight line). The linear one is tangent to the circle track. Say the two cars start from the point of tangency and have identical starts in the same direction travelling 10ft/s. We are wondering how fast will the angle between the two cars, as viewed from the circle, be changing when the black car is one-eight of the way around the circle.

That is the exact wording. I'm not exactly sure of the relationship you are talking about. Do you mean the fact that the angle is 90 degrees between tangent and chord?
Click to expand...
No, a problem given to you would not say, "we are wondering". And if this is not an assignment, then you can just not bother doing it, because it is not worded clearly.

The relationship I refer to is between the two angles I marked on my picture. It is one of those discussed here.
 
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