A runner is following the path $=(e^{-t}cos(t),e^{-t}sin(t))$ for $t0$ in a field with a

temperature distribution given by $T(x,y)=60e^{-(x^2+y^2)}.$ Assume that the runner is wearing

a wristwatch with markings ranging from $T=0$ to $T=60.$

a$)$ Determine the rate of change of temperature the runner feels at all instances of time

$t=n$ for $n=1,2,3,$cdots

b$)$ Find the angular velocity of the watch's hand at these instances of time.