Two banked curves have the same radius. Curve A is banked at 12.7 °, and curve B is banked at an angle of 15.1°. A car can travel around curve A without relying on friction at a speed of 19.1 m/s. At what speed can this car travel around curve B without relying on friction?

20.88 m/s

Explanation:

Curve A:

theta = 12.7, vA = 19.1 m/s

Curve B:

Theta = 15.1 degree

Let the speed is v.

By the use of given formula

tanθ = v^2 / rg

For Curve A

tan 12.7 = (19.1) ^2 / r g ... (1)

For Curve B

tan 15.1 = v^2 / r g ... (2)

Divide equation (2) by equation (1), we get

tan 15.1 / tan 12.7 = v^2 / (19.1) ^2

0.269 / 0.225 = v^2 / 364.81

v = 20.88 m/s