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17 August, 08:44

A car tire has a radius of 1.5 feet. If the tire is rotating at 800 rpm, what is the speed of the car in miles per hour (1 mile = 5,280 feet) ? Round the answer to the nearest tenth.

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  1. 17 August, 11:09
    0
    The first the is to find the distance covered when the wheel makes one rotation.

    circumference = 2π*1.5=9.424778 feet

    In one minute the car would cover (9.424778*800) = 7,539.822369 feet

    Speed = distance/time

    time = 1 minute = (1/60) hours

    distance = (7,539.822369/5280) = 1.427996661 miles

    ∴ speed = 1.427996661: (1/60)

    = 85.7 miles per hour
  2. 17 August, 11:15
    0
    Radius = r = 1.5 feet

    Angular velocity = w = 800 rpm = 800 revolutions per minute

    Angular velocity = w = 800 x 2π radians per minute

    w = 1600π radians per minute

    Linear velocity = speed = v = r w

    So,

    v = 1.5 x 1600π feet per minute

    v = 2400π feet per minute

    v = 2400π x 60/5280 miles per hour

    v = 85.7 miles per hour

    So, the speed of the car is 85.7 miles per hour
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