Question

At what speed will a car round a 52-m-radius curve, banked at a 45???? angle, if no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s2)a. 27 m/s

b. 17 m/s
c. 23 m/s
d. 35 m/s

Answer 1

c. 23 m/s

Step-by-step explanation:

`\theta` = Angle of banking = 45°

r = Radius of turn = 52 m

g = Acceleration due to gravity = 9.81 m/s²

v = Velocity of car

As the car is tilted we have the relation

`tan\theta=(v^2)/(rg)\\\Rightarrow v=√(tan\theta rg)\\\Rightarrow v=√(tan45* 52* 9.8)\\\Rightarrow v=22.57432\ m/s\approx 23\ m/s`

The velocity of the car is 23 m/s if the car is not slipping