Question

A car of mass 1500 kg goes over hill at a high speed. The shape of the hill is approximately circular, with a radius of 60 m, as in the figure. When the fastest that car can pass over the highest point of the hill without flying off the road?

Answer 1

The car can pass over the highest point of the hill without flying off the road at a speed of approximately 24.2 m/s.

Step-by-step explanation:

The car will fly off the road at the top of the hill when its weight exceeds the centripetal force keeping it in a circular path. To find the maximum speed, we equate the weight with the centripetal force:

Weight = Centripetal force

m * g = m * (v^2 / r)

Simplifying and solving for v, we get:

v = sqrt(g * r)

Substituting the given values, we have:

v = sqrt(9.8 m/s^2 * 60 m) = sqrt(588) m/s ≈ 24.2 m/s

Therefore, the fastest the car can pass over the highest point of the hill without flying off the road is approximately 24.2 m/s.