Final answer:
The ideal banking angle for a turn can be calculated using the formula tan(θ) = v² / (r * g), which is derived from the balance between centripetal force and gravitational force.
Step-by-step explanation:
To calculate the angle at which the turn should be banked for a radius of 120 m at a speed of 35 m/s, we use the formula for the banking angle, which is derived from equating the centripetal force to the component of the gravitational force:
tan(θ) = v2 / (r * g) where:
- v is the speed (35 m/s),
- r is the radius of the turn (120 m),
- g is the acceleration due to gravity (approximately 9.81 m/s2).
Plugging the values into the equation gives us the ideal banking angle:
tan(θ) = (35 m/s)2 / (120 m * 9.81 m/s2)
θ = tan-1((352) / (120 * 9.81))