Final answer:
The ideal speed for taking a 100.0-m-radius curve banked at a 20.0° angle is calculated using the formula v = √(rg tanθ), yielding approximately 14 m/s.
Step-by-step explanation:
The student is asking about the ideal speed to take a 100.0-m-radius curve banked at a 20.0° angle. To calculate the ideal speed (v) for a banked curve, we can use the formula v = √(rg tanθ), where 'r' is the radius of the curve, 'g' is the acceleration due to gravity (9.8 m/s² on Earth), and 'θ' is the angle of the bank.
Plugging in the given values, we get:
v = √(100 m * 9.8 m/s² * tan(20.0°)).
After calculating, we find that the ideal speed is approximately 14 m/s.