Final answer:
To find the angular position on a rotating Ferris wheel after 65 seconds, calculate the number of rotations made and the position within the final rotation, resulting in an angular position of approximately 86.4 degrees from the start point.
Step-by-step explanation:
To determine your angular position on a Ferris wheel 65 seconds after it starts turning, you need to calculate how many complete rotations you've completed in that time, and then find the position within the final partial rotation. The wheel completes a rotation every 29 seconds, so in 65 seconds, it completes ≈ 2.24 rotations. To find the exact angular position, you take the fractional part (0.24 of a rotation) and multiply it by 360° (since a full rotation is 360°). Thus, your angular position is about 86.4° from the initial bottom position after 65 seconds.