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Apersondesirestoreacha pointthatis3.42kmfromher presentlocationand in a directionthat is 35.0°northof east

However,shemusttravelalongstreetsthatgoeithernorth- southoreast-west.What is the minimumdistanceshecould travel to reachher destination?

6 years ago

We also assume that the angle subtended by the vector with respect to the positive x axis, along the unite vector is represented by .

Given:

The figure below shows the vector , directed at 35.0° north of east. The components of the vectors are also shown in the figure. The horizontal component of vector is given as whereas the vertical component (a

It is important to note that the magnitude of the component of vector represents the shortest distance that the person should travel to reach her destination in minimum time, However, with the constraints of moving either north-south or east-west, the minimum distance will be equal to the sum of horizontal component of vector and the vertical component of vector

The horizontal vector component of vector is:

Substituting the given values, we have

The vertical vector component of vector is:

Substituting the given values, we have

Therefore the person must walk 1.96 km east and 2.80 km north to reach her destination.

The total distance (say s) traveled by the person is:

s = a

= 2.80 km + 1.96km

The person can choose to either walk north first and then east, however this does not affect the distance she travels.

Therefore the total minimum distance traveled by the person is 4.76km.

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