A runner’s resultant velocity is 8 miles per hour due west running with a wind of 3 miles per hour N 28° W. What is the runner’s speed, to the nearest mile per hour, without the effect of the wind.

7.07 miles/hour W 22° S.

Step-by-step explanation:

Given that the resultant velocity of the runner, miles/hour due west.

Wind speed, miles/hour N 28° W.

Assuming that the absolute velocity of the runner, miles/ hour W \alpha S as shown in the figure.

By using vector addition, .

Now, from the figure,

And

Dividing equation (ii) by equation (i), we have

Putting the value of \alpha in equation (ii), we have

miles/hour

Hence, the runner speed, without the effect of the wind, is 7.07 miles/hour W 22° S.

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