Differential Equation - Path of Dog Chasing a Rabbit running in a curved path

  1. 1. The problem statement, all variables and given/known data
    A rabbit starts at the origin and runs at speed a along the right branch of the parabola y = x2. At the same moment, a dog starts at the point (c,0) and runs at speed b directly towards the rabbit.
    Write a differential equation for the path of the dog.


    2. Relevant equations
    I'm assuming I have to find the slope of the tangent line of the dog's path at some point, factoring in the speeds of the animals.


    3. The attempt at a solution
    I'm pretty well stuck at the beginning on this one. I've drawn a diagram, but I'm not sure how to factor in the speeds of the animals. I understand the tangent line of the path of the dog at any time t0 would intersect the rabbit's position at the same time t0. I have set y = t2 and x = t. I know I don't have much done. Any help to get me started would be appreciated.
     
  2. jcsd
  3. Your idea for the dog's path seems correct.

    You still have to include the animals' speeds. So maybe forget about the dog first and try to get the rabbit's path with the right speed.
     
  4. hunt_mat

    hunt_mat 1,613
    Homework Helper

    I would compute the dogs position at t and t+dt, you will get a triangle of vectors and it should be clear at what the equation is.

    Mat
     
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