this is a question about ordinary diffrential question.can anyone helps me to solve it?

Question

imagine yourself at the junction.u saw someone 100 meter in front of you.you would like to catch him up.he is walking with a constant speed of v and you start walking until u reached a speed of 2v.what is your path?will you be able to catch up that guy?you have to setting up a diffrential equation.you can simplify the solutions of the diffrential equation by diffrentiating and then solve the first order diffrential equation.initially he is 100m at your south

he is moving to the west direction

Answer 1

I'll try. Velocity is a vector quantity. i is x direction, j is y.

let his v = -dx/dt i, your v = -dx'/dt i - dy/dt j,

So, -dy/dt (t) = -100 m
-dx/dt (t) = -d m
-dx'/dt (t) = -d m

By inspection, the velocities in the i direction have to be equal.

So for this example, -dx/dt i - dy/dt j = 2 dx/dt at the required angle.

Therefore, dy/dt = 3^0.5 dx/dt, so the direction would be 60 degrees south of west.

Answer 2

this isn't calculus, it's algebra.
Unless you can say in which direction he is moving, (toward, away, at an angle to you?) you really can't solve this one.

Answer 3

just run to catch him up. seriously i think yu would overtake him