The bicycle is traveling at 16.23 miles per hour. To calculate this, first convert the revolution rate to radians per minute (1 revolution = 2π radians). Then, use the formula v = ωr, where v is linear velocity, ω is angular velocity, and r is the radius. Convert the result to feet per minute and then to miles per hour using the given conversion factor (5280 ft = 1 mi).
To find the linear velocity (v) of the bicycle, we can use the formula v = ωr, where ω is the angular velocity in radians per minute, and r is the radius of the tires. The given angular velocity is 210 revolutions per minute, and since 1 revolution is equivalent to 2π radians, the angular velocity in radians per minute is 210 * 2π. The radius is given as 13.0 inches.
Angular velocity, ω=210revolutions/minute×2πradians/revolution
ω=420πradians/minute
Now, we can use the formula v = ωr to find the linear velocity:
v=(420πradians/minute)×(13.0inches)
v≈5460πinches/minute
To convert this velocity to feet per minute, we use the fact that 1 foot is 12 inches:
v≈ 5460π/12 feet/minute
To convert this to miles per hour, we use the conversion factor 5280 feet = 1 mile:
v≈ 5460π/12×5280 miles/hour
v≈ 5460π/63360 miles/hour
v≈16.23 miles/hour
Therefore, the bicycle is traveling at approximately 16.23 miles per hour.