Two banked curves have the same radius. Curve A is banked at an angle of 11°, and curve B is banked at an angle of 16°. A car can travel around curve A without relying on friction at a speed of 18.5 m/s. At what speed can this car travel around curve B without relying on friction?

Answer 1

tan α=ma₁/mg = (mv₁²/r)/mg= v₁²/rg
tan β=ma₂/mg = (mv₂²/r)/mg= v₂²/rg

tan α/ tan β= v₁²/v₂²
v₂ = v₁•sqrt(tan β/tan α)=18.5•sqrt(tan16/tan11)=
=22.47 m/s