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

bearsfan3054

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.

betel

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.

hunt_mat

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