Final answer:
To find the ideal banking angle for a turn with a radius of 1.20 km and a speed limit of 105 km/h, you must use the formula θ = arctan((v^2)/(rg)). After calculating the velocity in m/s and plugging in the values, you'll get the banking angle in radians, and convert it to degrees for the final answer.
Step-by-step explanation:
The question is asking about the ideal banking angle for a turn on a highway, which is a concept in Physics related to centripetal force and the forces acting on a vehicle when it is turning. To determine the ideal banking angle, one must consider the radius of the curve and the speed limit of the highway.
Using the given radius of 1.20 km and a speed limit of 105 km/h, the formula for calculating the ideal banking angle (θ) in radians can be expressed as θ = arctan((v^2)/(rg)), where v is the velocity in m/s, r is the radius in meters, and g is the acceleration due to gravity (9.8 m/s^2). It's important to first convert the speed into meters per second by dividing 105 km/h by 3.6, which gives us approximately 29.17 m/s. Plugging the values into the formula would give us the ideal banking angle. Remember to convert the final result from radians to degrees by multiplying with (180/π).
The use of the appropriate units and correct mathematical operations is crucial in finding the accurate banking angle, which is essential for ensuring safety and comfort for vehicles making the turn.