Question

A car speeds over a hill past point A, as shown in the figure. What is the maximum speed the car can have at point A such that its tires will not leave the track? Round to one decimal place and include units. Image:

Answer 1

see explanations below

Step-by-step explanation:

At the point when the car leaves the track, the reaction on the road is zero, meaning that the centrifugal force equals the gravitation force, namely

mv^2/r = mg

Solve for v in SI units

v^2 = gr = 9.81 m/s^2 * 14.2 m = 139.302 m^2/s^2

v = sqrt(139.302) = 11.8 m/s

Answer: at 11.8 m/s (26.4 mph) car will leave the track.