Alice throws a ball straight up with an initial speed of 40 feet per second from a height of 5 feet. a. find parametric equations that model the motion of the ball as a function of time. b. how long is the ball in the air. c. when is the ball at its maximum height? d. determine the maximum height of the ball. e. using microsoft mathematics or any other graphing facility, simulate the motion of the ball by graphing the equation found in part (a.) what do you observe? f. what did you learn from doing this exercise?

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants