An 800 kg car is going around a circular track that has a radius of 200 m and is banked at 30o. The track surface is icy and frictionless. At what speed must the car go to avoid skidding sideways?

Explanation:

When a car moves in a circular path on a banked track . The relation between the angle of banking and velocity of car is

tanθ = v²/r g

here v is the velocity of car

r is the radius of circular path

g is the acceleration due to gravity

Thus  v² = tanθ r g

or v² = tan30 x 200 x 9.8 = 1960/ = 1132

or v = 33.7 ms⁻¹

The car should not move with a speed greater than 33 ms⁻¹