Question

A boy travels \[10m\] due north and then \[7m\]due east. Find the displacement of the boy.

Answer 1

Hint:To solve this problem, we need to know what displacement is. The displacement can be defined as the overall change in the position of an object. Also, the displacement is a vector quantity and therefore we need to consider the directions given to determine the displacement.

Complete step by step answer:
We are given that first a boy travels \[10m\] towards the north. We can take the north direction as the $ + y$ axis and so we can take this displacement in the north direction as \[10\widehat jm\].After that he travels \[7m\] towards the east. We can take the east direction as the $ + x$ axis and so we can take this displacement in the east direction as \[7\widehat im\].
The total displacement is $\left( {7\widehat i + 10\widehat j} \right)m$. We know that the magnitude of a vector quantity $\left( {x\widehat i + y\widehat j} \right)$is given by $\sqrt {{x^2} + {y^2}} $.
Thus, the magnitude of the required displacement is given by:
$\sqrt {{7^2} + {{10}^2}} = \sqrt {49 + 100} = \sqrt {149} = 12.2m$

Thus, our final answer is: When a boy travels \[10m\] due north and then \[7m\] due east, his total displacement is $12.2m$.

Note:we have determined the displacement of a boy which is a vector quantity. We need to remember that displacement is a vector quantity and distance is a scalar quantity. Therefore, we do not need to consider the directions while determining the distance covered by the boy. We can add the distance covered in both the directions by the boy which is his total distance cover. This means that when a boy travels \[10m\] due north and then \[7m\]due east, the total distance covered by him is $10 + 7 = 17m$.