Suppose Lynette ride her bicycle due south at a rate of 16 miles per hour.If the wind blowing due west at 4 miles per hours ,what is the resultant velocity and direction of the bicycle?
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To find the resultant velocity and direction of the bicycle, we need to consider both Lynette's velocity (riding due south at 16 miles per hour) and the wind's velocity (blowing due west at 4 miles per hour).
1. First, let's break down Lynette's velocity into its northward and eastward components. Since she is riding due south, her northward velocity component is 0 miles per hour, and her eastward velocity component is -16 miles per hour. (Note that the negative sign indicates the direction is opposite to east.)
2. Similarly, let's break down the wind's velocity into its northward and eastward components. Since the wind is blowing due west, its northward velocity component is 0 miles per hour, and its eastward velocity component is -4 miles per hour.
3. Now, to find the resultant velocity, we can add up the northward and eastward components separately. Adding the northward components (0 + 0) gives us a total northward velocity component of 0 miles per hour. Adding the eastward components (-16 + (-4)) gives us a total eastward velocity component of -20 miles per hour.
4. Finally, we can combine the northward and eastward components to get the resultant velocity. In this case, the resultant velocity has a northward component of 0 miles per hour and an eastward component of -20 miles per hour.
Therefore, the resultant velocity of the bicycle is 20 miles per hour (magnitude) and it is directed due west.