Final answer:
To find the design speed of a train traveling on a curved track, use the formula: speed = sqrt(radius * acceleration_due_to_gravity * tan(banking_angle)).
Step-by-step explanation:
In this question, we are asked to determine the design speed of a train traveling on curved railroad tracks. We are given the radius of the curve, which is 500.0 m, and the angle of banking, which is 5.0°. To find the speed, we can use the formula:
speed = sqrt(radius * acceleration_due_to_gravity * tan(banking_angle))
Plugging in the given values, we have:
speed = sqrt(500.0 * 9.8 * tan(5.0°))
Calculating this expression gives us the speed of the train for which the tracks are designed.