How Fast Is Temperature Changing for a Particle on a Circular Path?

[maysenator]

Homework Statement

Suppose that the Celsius temperature at the point (x, y) in the xy plane is T(x,y) = xsin(2y)
and that the distance in the xy plane is measured in meters. A particle moving clockwise around the circle of radius 1m centered at the origin at the constant rate of 2 m/s

a. how fast is the temperature experienced by the particle changing in degrees C per meter at the point P(1/2 , (sqrt[3])/2) ?

b. how fast is the temperature expereinced by the particle changing in degrees C per second at P?

Homework Equations

T(x,y) = xsin(2y)

P(1/2 , (sqrt[3])/2)

The Attempt at a Solution

i can do all the other estimating change problems where it gives me a function, 2 points, and ds = some constant just fine. but when i look at this i get kind of lost. i see the solution starts out by finding u in the direction of motion but I am not really sure how to find what i need out of this problem. I would appreciate any insight or a nudge in the right direction.

Thanks so much!

 

[maysenator]

can someone just point me in the direction of finding the unit tangent vector in the direction of motion please? i don't need a entire solution