A $0\mathrm{.}100$ kg toy car is propelled by a compressed spring that starts it moving. The car follows the curved path. If the spring constant of the launcher was $125$ N$/$m$,$ and the spring was compressed $5$ cm for the launch.

a$.$How fast $($in m$/$s$)$ is the car going when leaves the launcher.

b$.$How fast is the car going if travels up a hill to a height of $0\mathrm{.}120$ m$?$

c$.$ The car then goes into a valley that carries it below the launcher. At the bottom it is going $3\mathrm{.}00$ m$/$s$.$ How far below the launcher is the bottom of the valley. Report your answer as a positive number in meters.