For Homework2, problem 10a in chapter 4. How would I go about proving that the path of the ball is a line?
Choose the origin of the coordinate system to be at the initial position of the ball. Now write down an equation for each of x(t) and y(t). The ratio y(t)/x(t) is the tangent of the angle (to the x-axis) made by the displacement vector at time t. You should find that the tangent is independent of time, and hence the angle is independnet of time. This requires that the ball be moving in a straight line.