Part C: $(20$ points each, $40$ points total$)$:

A $50\mathrm{.}0$ g toy car on a frictionless track is accelerated by a spring with spring constant, $k=20\mathrm{.}0\frac{(N)}{(m)}$ that had been compressed $10\mathrm{.}0$ cm $.$ The car then travels down a $50\mathrm{.}0$ cm high ramp, travels for a short distance then travels up a long hill until it reverses direction due to gravitational acceleration.

a$)$ What is the car's velocity immediately after being launched by the spring?

b$)$ What is the car's velocity after traveling down the $50\mathrm{.}0$ cm high ramp?

c$)$ What is the maximum height that the car reaches on the long hill?