A $1000-$kg roller$-$coaster car moves from point $1$ to point $2$ and then to point

$3.$

$($a$)$ What is the gravitational potential energy at points $2$ and $3$ relative to

point $1?($That is$,$ take y $=0$ at point $1.)$

$($b$)$ What is the change in potential energy when the car goes from point $2$

to point $3?$

$($c$)$ Repeat parts $($a$)$ and $($b$),$ but take the reference point $($y $=0)$ to be at

point $3$