Answer
$a_{tan}=4.1\frac{m}{s^2}$
$a_R=13\frac{m}{s^2}$
$\mu_s=1.4$
Work Step by Step
$v_f=270 \frac{km}{h}\times \frac{1000m}{1km}\times \frac{1h}{3600s}=75\frac{m}{s}$
Circumference=$2\pi r=2\pi \times 220m=1380m$
$\Delta t = \frac{1380m}{75\frac{m}{s}}=18.4s$
For half circle, we need to divide both values by 2
$\frac{75\frac{m}{s}}{2}=37.5\frac{m}{s}$
$\frac{18.4s}{2}=9.2s$
$a_{tan}=\frac{\Delta v}{\Delta t}=\frac{37.5\frac{m}{s}-0\frac{m}{s}}{9.2s}=4.1\frac{m}{s^2}$
$v=\sqrt{\frac{\big(75\frac{m}{s}\big)^2}{2}}=53\frac{m}{s}$
$a_R=\frac{v^2}{r}=\frac{\big(53\frac{m}{s}\big)^2}{220m}=13\frac{m}{s^2}$
$a=\sqrt{a_{tan}^2+a_R^2}=\sqrt{\big(4.1\frac{m}{s^2}\big)^2+\big(13\frac{m}{s^2}\big)^2}=14\frac{m}{s^2}$
$F_f=ma$
$\mu_s mg=ma$
$\mu_s=\frac{a}{g}=\frac{14\frac{m}{s^2}}{9.8\frac{m}{s^2}}=1.4$
