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# Suppose the designated speed for an exit ramp on a highway is to be $13.4\; m/s$ and the radius of the curve is $50.0\; m$. At what angle should the curve be banked? (i.e, the roadway is tilted towards inside of the curve).

$\begin{array}{1 1} 12.2^{\circ} \\ 20.1^{\circ} \\ 4.8^{\circ}\\ 2.9^{\circ}\end{array}$

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A)
Answer :$20.1^{\circ}$
However, if the road is banked at an angle $\theta$, Only the component $n= n \sin \theta$ causes the centripetal acceleration.
$\sum F_r = n \sin \theta= \large\frac{mv^2}{r}$-----(1)
Thus, from $\sum F_y =0$ we have
$n \cos \theta =mg$ ----------(2)
(3) $\tan \theta =\large\frac{v^2}{rg}$
$\theta = \tan ^{-1} \bigg( \large\frac{(13.4\;m/s)^2}{(50.0\;m)(9.80\;m/s^2)} \bigg)$$=20.1^{\circ}$