You will use vector functions to develop a simple model for 3-point basketball shots. To keep the model simple, we will be ignoring air resistance, friction, and other forces. Furthermore, by "scoring," we will mean that the ball falls straight into the basket on its way downward (i.e., we will ignore the possibility of the ball bouncing in off the backboard, or nay energy losses as a result of spins, etc.).

1. A basketball player is attempting a 3-pointer from a horizontal distance of 24.7 feet. He is releasing the ball from 7 feet above ground level, aimed directly toward the basket at an angle of elevation of 45, with an initial velocity of 0. Supposing that the player stands at the origin and the basket is in the positive y-direction, use the three-dimensional coordinate system to find a vector function describing the position of the ball after release as a function of time. (Assume one unit on each axis corresponds to a distance of 1 foot, and the gravitational acceleration = 32/ 2 .)