Question

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

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

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

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

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

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

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

Answer 1