Well, that's a slippery situation! We've got a car on a slick road, going around a curve without any friction. Talk about cutting corners! Let's get cracking and find that radius.
To solve this, we can use the equation:
radius = (velocity^2) / (g * tan(θ))
Where:
- velocity is the speed of the car, which is 24.0 m/s
- g is the acceleration due to gravity, which is around 9.8 m/s^2
- θ is the angle of banking, which is 30 degrees
So, let's crunch some numbers:
radius = (24.0^2) / (9.8 * tan(30))
Now, my trusty calculator seems to be a little shy, but it tells me that the radius of the curve is approximately 224.5 meters.
So, there you go! The radius of the curve is about 224.5 meters. Just remember, always keep an eye out for slippery roads and clown cars trying to impress you with their fancy acrobatics!