A tennis ball on an rubber string is swung around a pole located at (0,0), and it is making a path resembling an elliptical orbit. Note that the height of

the ball is being ignored in this example.) The path looks similar to that shown in the figure below. The location of the ball can be determined at any time t as: Find the position vector r(t) that represents the position of the ball at any time t. \text { Find the velocity vector } \mathbf{v}(t)=\frac{d \mathbf{r}}{d t} \text { that represents the velocity of the ball at any time } t \text {. } x=3 \cos t+\sin t, \quad \text { and } y=\cos t+1 \sin t At what time will the velocity be in the y direction only? Time t What time is the next time the velocity is only in the y direction? Time t