Short Answer 
To calculate the speed of each seat on a circular platform with a diameter of 7.33 meters, first find the radius (3.665 m) and then the angular velocity (1.614 rad/s) using the formula ω = √(g / r). Finally, the speed of each seat is calculated to be approximately 5.912 m/s using the formula v = rω.
Step 1: Calculate the Radius
To begin, we need to determine the radius of the circular platform. The radius (r) is half of the diameter. In this case, the diameter is 7.33 meters, so we calculate the radius as follows:
- r = 7.33 m / 2 = 3.665 m
Step 2: Determine the Angular Velocity
Next, we find the angular velocity (ω) using the formula: ω = √(g / r), where g is the acceleration due to gravity, approximately 9.8 m/s². By substituting the values, we can calculate the angular velocity:
- ω = √(9.8 / 3.665) = 1.614 rad/s
Step 3: Calculate the Speed of Each Seat
Finally, we can determine the speed of each seat (v) using the formula: v = rω. By substituting the previously calculated radius and angular velocity, we can find the speed:
- v = 3.665 m * 1.614 rad/s = 5.912 m/s