A car drives along a country road at a constant speed of 26 m/s.When it encounters a hill,its tires just barely leave the pavement as the car passes over the top of the hill.What is the radius of curvature of the hill?
A)69 m
B)81 m
C)250 m
D)Information about the mass of the car is needed.

Question

Quizplus · Accepted Answer

The radius of curvature of the hill can be found using the formula for centripetal acceleration $a = \frac{v^2}{r}$, where $a$ is the acceleration due to gravity (9.8 m/s$^2$) when the car just barely leaves the ground, $v$ is the velocity (26 m/s), and $r$ is the radius of curvature. Rearranging the formula to solve for $r$, we get $r = \frac{v^2}{a}$. Substituting the given values, $r = \frac{26^2}{9.8} \approx 69$ meters.

A Car Drives Along a Country Road at a Constant