Billy hit a baseball with an initial speed of 125 feet per second at an angle of 40° to the horizontal. The ball was hit at a height of 3 feet above the ground.

(a) Find parametric equations that model the position of the ball as a function of time.

(b) How long was the ball in the air?

(c) Determine the horizontal distance that the ball traveled.

(d) When was the ball at its maximum height? Determine the maximum height of the ball.

(e) Using a graphing utility, simultaneously graph the equations found in part (a).