Two banked curves have the same radius. Curve A is banked at 11.0 °, and curve B is banked at an angle of 17.4 °. A car can travel around curve A without relying on friction at a speed of 15.3 m/s. At what speed can this car travel around curve B without relying on friction?

Answer 1

r of A = r of B
θ of A = 11°
θ of B = 17.4°
v of A = 15.3 m/s
v of B = ?

tan(θA) = (vA^2)/(rg)
derive to: r = (vA^2)/(tan(θA))(g)
r=(15.3^2)/(tan11)(9.8)
r=122.8866 m

tan(θB) = (vB^2)/(rg)
derive to: vB=sqrt[(r)(tanθB)(g)]
vB=sqrt[(122.8866)(tan17.4)(9.8)]
vB=19.4268 m/s

Answer: vB = 19.43 m/s