Chasing Person B: Describing the Curve Mathematically

  • Thread starter hypermonkey2
  • Start date
  • Tags
    Curve
In summary, the conversation discusses a problem where two people, A and B, are moving with constant speeds towards each other. Person A is trying to chase person B who is moving in a straight line. They discuss the mathematical description of the curve created by this movement and whether or not person A will ever intercept person B. They also mention that the curve may have an asymptote and suggest looking at resources for mathematical analysis.
  • #1
hypermonkey2
102
0
Heres a problem that could use some light. Say person A at (0,1) is following a person B at (0,0). Person B moves horizontally with a constant speed v (towards the positive x direction). Person A also moves with speed v, but always in the direction pointing at person B (to chase him). How can we describe mathematically the curve thus created?

I hope my explanation of the problem was clear, thanks!
 
Last edited:
Physics news on Phys.org
  • #2
Do you think A will ever intercept B?
 
  • #3
I wouldn't think so. Their distance might become infinitely small though, if that means the same thing.
 
  • #4
So one property of the curve would be that it has an asymptote?
 
  • #5
That would seem to be the case. But even so, we haven't been able to solve the differential equation. Can you try a mathematical analysis? This is not homework, haha, no need for the socratic method.
 
  • #6
Have a look at http://mathworld.wolfram.com/PursuitCurve.html" .
 
Last edited by a moderator:
  • #7
thanks, ill wrestle with that.
 

1. What is "Chasing Person B: Describing the Curve Mathematically"?

"Chasing Person B: Describing the Curve Mathematically" is a mathematical problem often used to illustrate the concept of rate of change. It involves two people, one chasing the other at a constant speed, and aims to find the equation that describes the distance between them at any given time.

2. How is this problem solved?

The problem is typically solved using a system of equations. The first equation represents the distance between the two people, while the second equation represents their respective speeds. By solving the system for time, the equation for the distance can be found.

3. What is the significance of this problem?

"Chasing Person B: Describing the Curve Mathematically" is a commonly used example for teaching the concept of derivatives in calculus. It helps students understand how the rate of change of one variable can be related to another variable. It also has real-world applications, such as calculating the relative speed of two objects in motion.

4. Can this problem be solved with other methods besides using a system of equations?

Yes, there are other methods that can be used to solve this problem, such as using geometric or graphical approaches. However, using a system of equations is the most commonly used method and provides a more general solution that can be applied to other similar problems.

5. Are there any variations of this problem?

Yes, there are many variations of this problem that involve different scenarios, such as one person chasing another with a changing speed, or multiple people chasing each other in a circular motion. These variations can be more complex and may require different methods to solve them.

Similar threads

I Gradient Vectors: Perpendicular to Level Curves
    • Calculus
Replies
4
Views
2K
I Purpose of parametrization
    • Calculus
Replies
3
Views
975
B Mechanics behind curved time causing gravitation/geodesics
    • Special and General Relativity
Replies
27
Views
4K
I Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves
    • Beyond the Standard Models
3
Replies
72
Views
5K
Exploring Mental Blocks in Mathematics: A Personal Perspective
    • General Discussion
Replies
5
Views
929
I Acceleration through curved paths
    • Classical Physics
2
Replies
39
Views
3K
How Does Particle P Chase Particle Q on a Circular Path?
    • Introductory Physics Homework Help
2
Replies
35
Views
3K
B Understanding Momentum: The Relationship Between Mass, Velocity, and Force
    • Mechanics
Replies
29
Views
1K
I Curved spacetime bulging in time direction
    • Special and General Relativity
Replies
30
Views
646
Constant tangential speed along arbitrary parametric curve
    • Calculus
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top