- #1
SeattleDrew
- 12
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Homework Statement
A mouse starts at the origin and runs up the y-axis with a speed a. At the same time, a cat running with speed b, starts at the point (c,0) and pursues the mouse.
i. What is the path of the cat?
ii. Assume a<b and solve for y(x). How far does the mouse run before being caught by the cat?
iii. Assume a=b and solve for y(x). How close does the cat come to the mouse?
Homework Equations
Circled in red are the steps in the problem that I'm comfortable with (refering to the picture below). The rest of the math was from a friend who conceded that he wasn't sure if he was on the right track. If he was on the right track then I would benefit from somebody explaining why that's the right track and possibly hinting what to do next.
Relevant equations is likely where I'm stuck. I don't know how to approach the cat's movement towards the mouse. I understand that the mouse's position changes the cat's movement, but I don't see how to show that relationship using equations.
The Attempt at a Solution
One classmate suggested that we use Euler's Method, which I haven't used yet, but it doesn't make much sense to me since the cat could start from anywhere on (c,0). All we've done so far in class are first order DEs and Wronskian DEs.
Intuitively I want to say the answer to iii. is what ever the distance is when both the cat and mouse start. Is there a clean way to prove that? (My prof. likes proofs)I haven't taken Linear Algebra, but if you throw any terminology at me from LA I will do my best to find out what you mean.