The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the
Speedway banked?
A) $32 ^ { \circ }$
B) $26 ^ { \circ }$
C) $34 ^ { \circ }$
D) $28 ^ { \circ }$
E) $30 ^ { \circ }$

Question

The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the
Speedway banked? 
A) $32 ^ { \circ }$
B) $26 ^ { \circ }$
C) $34 ^ { \circ }$
D) $28 ^ { \circ }$
E) $30 ^ { \circ }$

Quizplus · Accepted Answer

The correct answer is A because the angle of banking is given by the equation tan(theta) = v^2 / rg, where v is the speed of the car, r is the radius of the curve, and g is the acceleration due to gravity. Plugging in the given values, we get tan(theta) = (34 m/s)^2 / (190 m * 9.8 m/s^2) = 0.602. Taking the arctangent of both sides, we get theta = 32 degrees.

The Curved Section of a Speedway Is a Circular Arc 32∘32 ^ { \circ }32∘

The Curved Section of a Speedway Is a Circular Arc $32 ^ { \circ }$