Question

a hiker walks 5 km due north and the 7 km due east .what is the magnitude of the resultant vector

Answer 1

Answer:

refer the attached photo

Explanation:

sorry if blur but my camera is not working properly

Answer 2

The magnitude of the resultant vector is equal to 8.602 metres.

Given:

The hiker walks 5 km due North and then walks 7 km due East.

To Find:

The magnitude of the resultant vector.

Solution:

→ As the hiker first walks 5 km due North and then walks 7 km due East. Therefore the magnitude of the net resultant vector would be equal to the vectorial sum of the two displacements.

→ Let us assume the North direction to be along the y-axis and the unit vector along the north direction be $\boldsymbol{\hat{\textbf{\j}}}$

→ Let us assume the East direction to be along the x-axis and the unit vector along the east direction be $\boldsymbol{\hat{\textbf{\i}}}$

→ The net displacement vector can be written as: $\boldsymbol{(7)\hat{\textbf{\i}}+(5){\hat{\textbf{\j}}}}$

→ Now, we would calculate the magnitude of the resultant vector:

∴ The magnitude of the resultant  = $\boldsymbol{\sqrt{5^{2}+ 7^{2} }=\sqrt{25+49}=\sqrt{74}\:\:metres }$

∴ The magnitude of the resultant = $\boldsymbol{\sqrt{74}=8.602\:metres }$

∴ The magnitude of the resultant vector would be equal to $\boldsymbol{8.602\:metres}$.

Therefore the magnitude of the resultant vector comes out to be equal to 8.602 metres.

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