Final answer:
Using the provided formula for the banking angle in a turn, the slope of the banked road for the vehicle traveling at 20 m/s on a 75 m radius turn is 30 degrees (Option D).
Step-by-step explanation:
To calculate the slope of the banked road where a vehicle travels, we can use the relationship between the angle of banking, the speed of the vehicle, the radius of the turn, and the acceleration due to gravity. The angle θ can be found using the formula θ = tan¹(v²/(rg)), where v is the speed of the vehicle, r is the radius of the turn, and g is the acceleration due to gravity (approximately 9.8 m/s²).
First, we will substitute the given values into the formula:
θ = tan¹((20 m/s)²/(75 m × 9.8 m/s²))
= tan¹(400/(735))
= tan¹(0.5442)
= 28.8° (approximately)
The closest answer to 28.8° from the options given is 30°, so the slope of the banked road is 30 degrees (Option D).