A car drives over a hilltop that has a radius of curvature 120 m at the top of the hill. At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?
A)45.5 m/s
B)41.8 m/s
C)34.3 m/s
D)22.2 m/s
E)27.6 m/s

Question

Quizplus · Accepted Answer

At the top of the hill, the gravitational force provides the necessary centripetal force for circular motion. The condition for the car to just barely lose contact is when the normal force is zero. Using the formula for centripetal force, $mg = \frac{mv^2}{r}$, we can solve for $v$: $v = \sqrt{gr}$. Substituting $g = 9.8 \, \text{m/s}^2$ and $r = 120 \, \text{m}$, we find $v \approx 34.3 \, \text{m/s}$.

A Car Drives Over a Hilltop That Has a Radius