Question

An exit ramp of a highway is banked at an angle of 27 degrees

. The radius of ramp is 200m,

what is the maximum possible speed of an exiting car?

Answer 1

$$Nsin\theta=\dfrac{mv^2}{R}, (1)$$ $$Ncos\theta=mg. (2)$$

Dividing equation (1) by (2), we get:

$$tan\theta=\dfrac{v^2}{Rg},$$ $$v_{max}=\sqrt{Rgtan\theta},$$ $$v_{max}=\sqrt{200\ m\cdot9.8\ \dfrac{m}{s^2}\cdot tan27^{\circ}}=31.6\ \dfrac{m}{s}.$$