A car with a mass of 1200 kg goes over a hill at a constant speed.The top of the hill can be approximated as an arc length of a circle with a radius of curvature of 210 m.What minimum speed must the car have as it passes over the top of the hill in order to become airborn?
A)9.8 m/s
B)11 m/s
C)37 m/s
D)45 m/s
E)56 m/s

Question

Quizplus · Accepted Answer

The minimum speed required for the car to become airborne at the top of the hill is the speed at which the normal force acting on the car is zero. At this point, the only forces acting on the car are gravity and the force of the road pushing up on the car. The normal force is given by:$$N = mg - mv^2/r$$where m is the mass of the car, g is the acceleration due to gravity, v is the speed of the car, and r is the radius of curvature of the hill.Setting N = 0, we get:$$mg - mv^2/r = 0$$Solving for v, we get:$$v = sqrt(rg)$$Substituting the given values, we get:$$v = sqrt(210 m * 9.8 m/s^2) = 45 m/s$$Therefore, the minimum speed the car must have as it passes over the top of the hill in order to become airborne is 45 m/s.

A Car with a Mass of 1200 Kg Goes Over