A roadway for stunt drivers is designed for racecars moving at a speed of 97 m/s. A curved section of the roadway is a circular arc of 420 m radius. The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero. At what angle is the roadway banked?

Banking angle is 66.35°

Explanation:

Given radius r=420m

Speed=97m/s

banking angle is A

Note before

(V) = √ (r*gtanA)

√97=√420*9.81*tanA) taking square of both sides

97^2=420*9.81*tan A.

tanA=66.35°

A=66.35°

Given that,

The speed of the car is

Vc = 97m/s

The radius of circular path of the car is

Rc = 420m

We want to find the angle of roadway banked β?

To determine the angle of roadway banked, we will use the formula

tanβ = Vc² / Rc•g

Where Vc = 97m/s, Rc = 420m and

g = 9.8m/s²

Then

tanβ = 97² / (420 * 9.8)

tanβ = 2.28596

β = ArcTan (2.28596)

β = 66.37°

The railway banked at an angle of 66.37°