Question

A highway curve with radius 80 m is to be banked so that a car traveling 21 m/s will not skid sideways even in the absence of friction. At what angle should the curve be banked?

Answer 1

Answer:

Angle, θ = 29.35

Explanation:

It is given that,

Radius of the curve, r = 80 m

Velocity of the car, v = 21 m/s

The highway curve is to be banked so that the car will not skid sideways in the presence of friction. We need to find the angle should the curve be banked. Let the angle is θ. It is given by :

$tan{\theta}=\dfrac{v^2}{rg}$

Where

g = acceleration due to gravity

$tan\ {\theta}=\dfrac{(21\ m/s)^2}{80\ m\times 9.8\ m/s^2}$

$\theta=tan^{-1}(0.5625)$

θ = 29.35°

Hence, this is the required solution.