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Chapter 3: Problem 13

A girl delivering newspapers covers her route by traveling \(3.00\) blocks west, \(4.00\) blocks north, and then \(6.00\) blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

Short Answer

Expert verified
The resultant displacement of the girl's route is \(5.00\) blocks in a North-East direction. The total distance she travels is \(13.00\) blocks.

Step by step solution

01

Defining Directional Movements

Firstly, it needs to be understood that movement West is in the opposite direction to that of East. The blocks have been given as units so they are dimensionless. We have \(3.00\) blocks West, \(4.00\) blocks North, and \(6.00\) blocks East. Thus, the net movement in the east-west direction can be calculated as the difference of movements in East and West. This is \(6.00 - 3.00 = 3.00\) blocks to the East.
02

Resultant Displacement

The resultant displacement is the vector sum of the east-west movement and the north movement. Since our east-west movement is \(3.00\) blocks to the East, and our north movement is \(4.00\) blocks, we can represent these two vectors as perpendicular vectors in a 2-D plane. We can use the Pythagorean theorem to calculate the magnitude of the resultant displacement: \( \sqrt{(movement \, east)^2 + (movement \, north)^2} = \sqrt{(3.00^2 + 4.00^2)} = 5.00 \) blocks. This displacement is in the North-East direction as obtained by resolving the vectors.
03

Total Distance

The total distance is simply the sum of the lengths of all the individual movements the girl made, regardless of the direction. Thus, adding up all the blocks she traveled: \( 3.00 + 4.00 + 6.00 = 13.00 \) blocks.

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Most popular questions from this chapter

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