Final answer:
The speed at which these tracks are designed for trains can be calculated using the formula Speed = √(g * r * tan(θ)).
Step-by-step explanation:
The speed at which these tracks are designed for can be determined using the concept of centripetal force and the angle of banking. The formula to calculate the speed is:
Speed = √(g * r * tan(θ))
where g is the acceleration due to gravity (9.8 m/s²), r is the radius of the curve (500.0 m), and θ is the angle of banking (5.0°).
Substituting the given values into the formula:
Speed = √(9.8 * 500.0 * tan(5.0°)) = 35.1 m/s
Therefore, these tracks are designed for trains traveling at a speed of 35.1 m/s.