1. **State the problem:** A ball rotates 5.76 times every 16 feet and moves at a speed of 61.56 km/h. We want to find how many times it rotates every minute. 2. **Convert speed to feet per minute:** - First, convert 61.56 km/h to feet per hour: $$61.56 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{3.28084 \text{ ft}}{1 \text{ m}} = 61.56 \times 1000 \times 3.28084 = 202,064.9 \text{ ft/h}$$ - Then convert feet per hour to feet per minute: $$\frac{202,064.9 \text{ ft}}{60 \text{ min}} = 3,367.75 \text{ ft/min}$$ 3. **Calculate rotations per foot:** - Given 5.76 rotations every 16 feet, rotations per foot is: $$\frac{5.76}{16} = 0.36 \text{ rotations/ft}$$ 4. **Calculate rotations per minute:** - Multiply rotations per foot by feet per minute: $$0.36 \times 3,367.75 = 1,212.39 \text{ rotations/min}$$ **Final answer:** The ball rotates approximately $1,212.39$ times every minute.