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

Answer:

c. 23 m/s

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

$tan\theta=\dfrac{v^2}{rg}\\\Rightarrow v=\sqrt{tan\theta rg}\\\Rightarrow v=\sqrt{tan45\times 52\times 9.8}\\\Rightarrow v=22.57432\ m/s\approx 23\ m/s$

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