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: z = 7 cost + sin t, and y = cost + 3 sint. NOTE: Give answers rounded to two decimal places, and use radians in all questions. a) c) Find the position vector r(t) that represents the position of the ball at any time t. E(t) =(_ At what time will the velocity be in the y direction only? Time t = Note: Give the smallest or first time only. What time is the next time the velocity is only in the y direction? b) dr that represents the velocity of the ball at any time dt Time t = Find the velocity vector v(t)= v(t) =(_

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: z = 7 cost + sin t, and y = cost + 3 sint. NOTE: Give answers rounded to two decimal places, and use radians in all questions. a) c) Find the position vector r(t) that represents the position of the ball at any time t. E(t) =(_ At what time will the velocity be in the y direction only? Time t = Note: Give the smallest or first time only. What time is the next time the velocity is only in the y direction? b) dr that represents the velocity of the ball at any time dt Time t = Find the velocity vector v(t)= v(t) =(_