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Chapter 2: Problem 5

A person desires to reach a point that is \(3.42 \mathrm{~km}\) from her present location and in a direction that is \(35.0^{\circ}\) north of east. However, she must travel along streets that go either northsouth or east-west. What is the minimum distance she could travel to reach her destination?

Short Answer

Expert verified
To find the minimum distance to be traveled, add up the calculated horizontal (east) and vertical (north) distances.

Step by step solution

01

Break destination into components

The destination is at \(35.0^{\circ}\) north of east, which means we can break it into east and north components. The north component denotes how much she will travel in the north direction, while the east component denotes east direction travel. The east component can be calculated using cosine of the angle, which gives the adjacent side in a right triangle. Hence, east component = \(3.42 \mathrm{~km} \times \cos(35.0^{\circ})\). Similarly, the north component can be calculated using sine of the angle, which gives the opposite side in a right triangle. Hence, north component = \(3.42 \mathrm{~km} \times \sin(35.0^{\circ})\).
02

Calculate individual distances

Now, calculate the distances based on the above formulae. The east component corresponds to the horizontal distance, and the north component corresponds to the vertical distance. Use a calculator to fetch these values.
03

Calculate total distance travelled

Once we get the individual distances traveled in the east and north direction, add them together. This gives the total distance traveled by the person in the city grid.
04

Interpretation of the result

The sum of the distances traveled in the east and north directions will give the minimum distance required to reach the desired spot by traveling either north-south or east-west.

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Most popular questions from this chapter

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