How Does the Angle Affect the Height and Speed of a Toy Car on a Track?

[Supremetheking]

1. Homework Statement

A toy car coasts along he curved track shown above. The car has initial speed vA when it is at point A at the top of the track, and the car leaves the track at point B with speed vB at an angle ϴ above the horizontal. Assume that the energy losses due to friction is negligible.
(a) Suppose the toy car is released from rest at point A (vA = 0).
i. After the car leaves the track and reaches the highest point in its trajectory it will be at a different height than it was at point A. Briefly explain why this is so. ii. Determine the speed of the car when it is at the highest point in its trajectory after leaving the track, in terms of vB and ϴ. Briefly explain how you arrived at your answer.
(b) Suppose the toy car is given an initial push so that it has nonzero speed at point A. Determine the speed vA of the car at point A such that the highest point in its trajectory after leaving the track is the same as its height at point A. Express your answer in terms of vB and ϴ. Explain how you arrived at your answer.

Homework Equations

Conservation of Energy

The Attempt at a Solution

I was able to find the speed of the highest point of the car after leaving the track, but part 1a, I think that the angle would affect it, but I don't know how. For part c I don't know how to make it consist of only Vb and theta.

 

[haruspex]

part 1a, I think that the angle would affect it,

Yes, it would. In fact, the question is not quite correct. There is an angle at which it would regain the same height.
Think about total energy, PE+KE.

For part c I don't know how to make it consist of only Vb and theta.

Please post your working as far as you got.

 

[Supremetheking]

Oh for part c, i got now after using the conservation of energy. I made a mistake while solving it before, which led me to not have Vb and theta only.
Part a, I got it too now, since only 90 degrees would allow it to be the same height, but since the angle in the picture doesn't show 90 degrees, but a angle of theta, we know that it won't reach the same height, since the vertical PE is converted to horizontal KE.
Thanks for helping!