Answer
(a) $v_{min}=19.32m/s$
(b) $v_{max}=23.45m/s$
Work Step by Step
1) Find $\tan\theta$
Take $d$ to be the difference between the largest and the smallest radius, we have $d=165-112=53m$
From the figure, we can see that $$\tan\theta=\frac{h}{d}=\frac{18}{53}=0.34$$
The formula for a banked curve is $$\tan\theta=\frac{v^2}{rg}$$ $$v=\sqrt{\tan\theta rg} (1) $$
(a) $v_{min}$ will correspond to $r_{min}=112m$. Apply equation (1):
$$v_{min}=\sqrt{0.34\times112\times9.8}=19.32m/s$$
(b) $v_{max}$ will correspond to $r_{max}=165m$. Apply equation (1):
$$v_{max}=\sqrt{0.34\times165\times9.8}=23.45m/s$$
