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?

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°

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°