Answer
The car's maximum speed without flying off the road is 22 m/s.
Work Step by Step
To find the maximum speed, we can assume that the gravitational force on the car is exactly equal to the required centripetal force to keep the car moving in a circular motion over the top of the hill.
$F_c = \frac{mv^2}{r} = mg$
$v^2 = gr$
$v = \sqrt{gr}$
$v = \sqrt{(9.80~m/s^2)(50~m)}$
$v = 22~m/s$
The car's maximum speed without flying off the road is 22 m/s.
