A roller$-$coaster $($as shown figure$)$ has a mass of $500kg$

when fully loaded with passengers. The path of the

coaster from its initial point shown in the figure to point

$($B$)$ involves only up$-$and$-$down motion $($as seen by the rid$-$

ers$),$ with no motion to the left or right. $($a$)$ If the vehicle

has a speed of $20\mathrm{.}0\frac{m}{s}$ at point $($A$),$ what is the force

exerted by the track on the car at this point? $($b$)$ What is

the maximum speed the vehicle can have at point $($B$)$

and still remain on the track? Assume the roller$-$coaster

tracks at points $($A$)$ and $($B$)$ are parts of vertical circles of

radius $r_1=10\mathrm{.}0m$ and $r_2=15\mathrm{.}0m,$ respectively.