Answer
$v = 100~km/h$
Work Step by Step
We can express the car's speed in units of $m/s$:
$v = (114~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 31.67~m/s$
We can find the angular speed:
$\omega = \frac{v}{r}$
$\omega = \frac{31.67~m/s}{100~m}$
$\omega = 0.3167~rad/s$
We can find the cheetah's linear speed:
$v = \omega~r$
$v = (0.3167~rad/s)(92~m)$
$v = 29.1364~m/s$
$v = (29.1364~m/s)(\frac{1~km}{1000~m})(\frac{3600~s}{1~h})$
$v = 100~km/h$
