8. A cart slides down an inclined plane with the angle of theincline θ starting from rest. At the moment the cart begins tomove, a ball is launched from the cart perpendicularly to theincline.

(a) Choosing an x-y-coordinate system with the x-axis along theincline and the origin at the initial location of the cart, derivethe equation of the trajectory that the ball assumes from theperspective of this coordinate system.

(b) Determine where the maximum of this trajectory is locatedand at what location along the chosen x-axis the ball will fallback into the cart.

(c) Sketch the trajectory in this coordinate system. What doesthe trajectory look like in an x-y-coordinate system where thex-axis is horizontal?

9. We discussed in lecture that from the perspective of a viewerin the cart sliding down the incline, the ball will always be seenas hovering above the cart, ultimately falling back into the cart.Describe what a viewer sitting in the classroom would see. Are thecart and the ball still advancing in lockstep from thatperspective? To help you put this into numbers, calculate where theball and cart will be located (x- and y-coordinate of each)

(a) at a time equal to the flight time to the peak of theparabolic trajectory and

(b) at twice the flight time to the peak. We choose an angle ofthe incline of 30o and v .