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A car wheel with a diameter of 27 inches makes 11,208 revolutions in 59 minutes. Find the linear velocity to the nearest tenth.

Answer :

Final answer:

The linear velocity of a car wheel that makes 11208 revolutions in 59 minutes, where the wheel has a diameter of 27 inches, is approximately 22.4 ft/s or roughly 15.3 mph.

Explanation:

we will need to know two things: the formula that relates the linear velocity of the car's wheel to its radius and revolutions per time unit, and how to convert different units appropriately.

Linear velocity can be defined as the product of the radius and the angular velocity of the wheel (angular velocity is merely the revolutions made per time unit but in radians). This can be expressed as follows: V = r * w, where V is the linear velocity, r is the radius of the wheel, and w is the angular velocity.

Since we know both the radius (half the diameter of the wheel: 27 inches / 2 = 13.5 inches, which in feet is about 1.125 feet, as 1 foot = 12 inches), and the angular velocity (11208 revolutions per 59 minutes), we can just fill these values into the formula.

However, firstly we need to convert our angular velocity into a standard measurement unit (e.g. rad/s), but let's first convert minutes into seconds: 59 minutes = 3540 seconds. Now, since 1 revolution corresponds to 2π radians, 11208 revolutions would correspond to 11208 * 2π = 70371.8 radians. Therefore, our angular velocity in rad/s is: 70371.8 rad / 3540 s = approximately 19.9 rad/s.

With all the required data converted into the correct units, we can substitute these values into our original formula (V = r * w) and find that V = 1.125 ft * 19.9 rad/s. Thus, your car wheel's linear velocity is approximately 22.4 ft/s (feet per second). If you want to convert this into miles per hour, the result is: 22.4 ft/s * 0.6818 = approximately 15.3 mph.

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