Final answer:
To calculate the maximum speed on a banked curve without lateral acceleration, use the relationship given by the equation v = √(tan(θ) × rg), where θ is the angle of banking, r is the radius of the curve, and g is the gravitational acceleration.
Step-by-step explanation:
The maximum speed at which a vehicle may travel on a banked curve without experiencing a net lateral acceleration can be found using principles from physics that relate to centripetal force and gravity. For a frictionless banked turn, the gravitational component of the force down the slope must provide the necessary centripetal force to keep the car moving in a circle. This condition is represented by the equation tan(θ) = {v^2 / (rg)}, where θ is the banking angle, v is the velocity, r is the radius of the curve, and g is the acceleration due to gravity (9.8 m/s^2). To find the maximum speed (v), we rearrange the equation to v = √(tan(θ) × rg). Substituting the given values (θ = 73 degrees, r = 240 m) and using the gravitational constant, we calculate the maximum speed without lateral acceleration.