Final answer:
The radius of the tire can be found using the formula ·v = r·ω·, where ·v· is the linear velocity and ·ω· is the angular velocity. With an angular velocity calculated from 10 revolutions per second, the tire's radius is approximately 24.6 cm.
Step-by-step explanation:
To find the radius of the tire given its rate of revolutions per second and its linear velocity, we can use the relationship between linear velocity (·v·), tire radius (·r·), and angular velocity (·ω·), which is ·v = r·ω·. The angular velocity can be calculated from the rate of full revolutions per second by converting revolutions per second to radians per second using the fact that one revolution is · 2π· radians.
First, let's calculate the angular velocity. Since the tire turns at a rate of 10 revolutions per second, we multiply by 2π to convert to radians per second: ·ω· = 10 revolutions/sec × 2π rad/revolution = 20π rad/sec.
Now, we apply the equation ·v = r·ω· to solve for the radius: ·r = v/ω·. Plugging in the values we have: ·r = 15.5 m/s / (20π rad/sec)·.
Calculating the radius, we get: r = 15.5 / (20π) = 0.246 m or approximately 24.6 cm.
Therefore, the radius of the tire is about 24.6 cm.