Problem $3$: A $150-$lb skater passes point A with a speed of $\backslash (6\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Equation of the curve for the track and other relevant information is given in Figure $3.$ Neglect Friction and determine the following:

$1.$ Skater's speed upon reaching point B$?(5$ points$)$

$2.$ Normal force exerted on skater by the track at this point B$?(5$ points$)$

$3.$ Skater's acceleration at B in Cartesian coordinates. That is in $\backslash (\backslash$hat$\{\backslash$imath$\}\backslash )$ and $\backslash (\backslash$hat$\{\backslash$boldsymbol$\{$j$\}\}\backslash )?(10$ points$)$

$4.$ Time required for a person to travel from point $\backslash ($ A $\backslash )$ to $\backslash ($ B $\backslash )?(15$ points$)$

Figure $3$: Problem $3$