167.08Formula: Angular velocity = 2π * frequency
frequency = 4.9 / 5 seconds = 0.98 / second
Angular velocity = 2π radian * 0.98/sec = 6.1544 radian / sec
To pass it to radian per hour multiply by the factor 3600 sec / hour
=> 6.1544 rad / sec * 3600 sec / hour = 22,155.84 rad/hour.
Now, you have to realize that the answer choices are not angular velocities. They have units of miles per hour, which means that they are linear velocities
To calculate linear velocities you need the radius of the circular path described by the object.
With the radius, then you use the formula V = angular velocity * radius =>
For example if the radius is 0.0402 miles, the linear velocity is 0.00402 miles * 22,155.84/hour = 89 miles per hour
If the radius is 0.00528 miles, V = 0.00528 miles * 22,155.84 / hour = 117 mph
If the radius is 0.00673 miles, V = 0.00673 miles * 22,155.84 / hour = 149 mph
If the radius is 0.00582 miles, V = 0.00582 miles * 22,155.84 / hour = 129 mph.
Now you know how to calculate the angular and linear velocities.
