Final answer:
The ideal banking angle for a turn with a 1.20 km radius at a 105 km/h speed limit can be found using the banked curve formula, resulting in an angle of approximately 15 degrees.
Step-by-step explanation:
To find the ideal banking angle for a gentle turn on a highway, we can use the formula for a banked curve without friction, which is θ = tan⁻¹(v²/rg), where θ is the banking angle, v is the velocity, r is the radius of the turn, and g is the acceleration due to gravity (approximately 9.81 m/s²). Let's calculate the banking angle for a turn with a 1.20 km radius at a speed of 105 km/h (which is equivalent to 29.17 m/s).
Firstly, we convert the speed limit to meters per second by dividing 105 km/h by 3.6:
v = 105 km/h ÷ 3.6 = 29.17 m/s
Then, we can plug the values into the formula:
θ = tan⁻¹((29.17 m/s)² / (1.20 km × 1000 m/km × 9.81 m/s²))
After calculating the above expression, we find that the ideal banking angle for this turn is approximately 15 degrees.