Final answer:
The speed of the ball is approximately 16.15 m/s.
Step-by-step explanation:
First, we need to calculate the angular speed of the ball. The ball revolves 5 times every 3.50 seconds, so we can calculate the time it takes for 1 revolution by dividing 3.50 seconds by 5. This gives us 0.70 seconds per revolution. Next, we calculate the angular speed of the ball by dividing 2π radians (a full revolution) by the time it takes for 1 revolution. So the angular speed is 2π/0.70 ≈ 8.97 rad/s.
Finally, we can find the speed of the ball using the formula v = rω, where v is the speed, r is the radius of the circle, and ω is the angular speed. Plugging in the given values, we have v = 1.80 m * 8.97 rad/s ≈ 16.15 m/s.
Therefore, the speed of the ball is approximately 16.15 m/s.