A highway is being constructed to accommodate traffic for speeds of 12.2 m/s. If the angle of the bank is 7.97° and there is no friction force, what is the highway's curve radius? 1.06×103 m 8.89 m 15.3 m 108 mQuestion 2A girl with a 59.4 g yo-yo is swinging it in a horizontal circle at an angular velocity of 7.86 rad/s. If the string is tilted down at an angle of 25.1°, what must the length of the yo-yo string be? 0.0222 m 0.0382 m 0.374 m 0.175 mQuestion 3A 2.50 kg toy race car is slowing down while travelling around a circular horizontal track. If the track has a diameter of 1.73 m and the coefficient of rolling friction between the track and the race car is 0.280, what is the magnitude of angular acceleration? 0.324 rads/s2 1.59 rads/s2 3.17 rads/s2 0.162 rads/s2

Sure, I can help with that. Here are the solutions to your problems:

Question 1: The formula for the radius of a banked curve without friction is r = v^2/g*tan(θ), where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the bank.

Substituting the given values, we get r = (12.2 m/s)^2 / (9.8 m/s^2 * tan(7.97°)) = 108 m. So, the correct answer is 108 m.

Question 2: The formula for the length of the yo-yo string is L = mg/(ω^2cos(θ)), where m is the mass of the yo-yo, g is the acceleration due to gravity (9.8 m/s^2), ω is the angular velocity, and θ is the angle of the string.

Substituting the given values, we get L = (0.0594 kg * 9.8 m/s^2) / ((7.86 rad/s)^2 * cos(25.1°)) = 0.175 m. So, the correct answer is 0.175 m.

Question 3: The formula for the magnitude of angular acceleration is α = μ*g/r, where μ is the coefficient of rolling friction, g is the acceleration due to gravity (9.8 m/s^2), and r is the radius of the track.

Substituting the given values, we get α = 0.280 * 9.8 m/s^2 / (1.73 m / 2) = 3.17 rads/s^2. So, the correct answer is 3.17 rads/s^2.