A Ferris Wheel's Height

📌 CONCEPT: The problem involves finding the angle at which a passenger on a rotating Ferris wheel is located, given the time spent on the ride and the height above the ground.

📐 RULE / FORMULA: To solve this, we use the formula for calculating the angle in radians, which is θ = ωt, where θ is the angle, ω is the angular velocity, and t is the time.

💡 WORKED EXAMPLE: A Ferris wheel with a radius of 25 meters is rotating at π/4 radians per minute. A passenger has been on the ride for 8 minutes and is currently at a height of 15 meters above the ground. We need to find the angle from the bottom of the wheel. First, we convert the height to a fraction of the radius: 15 / 25 = 3/5. Then, we use the formula for the height of a point on a circle: h = r cos(θ), where h is the height, r is the radius, and θ is the angle. Solving for θ, we get θ = arccos(3/5) ≈ 0.942 radians.

⚠️ COMMON MISTAKE: Students often forget to convert the given height to a fraction of the radius or misuse the formula for the height of a point on a circle, leading to incorrect angle calculations.