A toy car rolls along a curved track as shown below. The track has a tall incline that gradually slopes downward to a ramp that makes a 40 angle with the horizontal. The car is placed at point A, at the top of the track, and has initial speed v_A when it is at point A. It exits the track at point B with speed v_B. Assume that the rotational kinetic energy of the car's wheels and energy losses due to friction are both negligible.

a. Suppose the toy car is released from rest at point A (v_A = 1.0 m/s ).

i. The car exits the track at point B and reaches the highest point in its trajectory. Will the car's highest height be at a different height than it was at point A? Briefly explain.

ii. Consider the car when it is at the highest point in its trajectory after exiting the track. Determine the speed of the car in terms of v_B and θ¸. Briefly explain  your answer.

b. Suppose you want the car to exit the track and reach the same trajectory height as point A. You give the car an initial push so that at point A it has a nonzero speed. Determine the speed v_A of the car at point A so that the highest point in its trajectory is the same as its height at point A. Express your answer in terms of v_B and θ. Explain how you arrived at your answer.

A B