Question

A body moves 6m north, 8m east and 10m vertically upwards, what is its resultant displacement from initial position:
(A) $10\sqrt 2 m$
(B) $10m$
(C) $\dfrac{{10}}{{\sqrt 2 }}m$
(D) $10 \times 2m$

Answer 1

Hint: This could be simply solved by having some basic idea about direction. And also, some knowledge about components is needed. We need to use the components of the displacement to find the displacement vector and from there we can calculate the magnitude.
Formula used: Here, we will use the basic formula of speed, distance and time:
${{\text{V}}_{{\text{avg}}}}{\text{ = }}\dfrac{{\text{D}}}{{\text{T}}}$
Here, ${{\text{V}}_{{\text{avg}}}}$ is the mean speed of the car
${\text{D}}$ is the total distance travel
$T$ is the travel time

Complete step by step answer:
We will start by noting the values provided,
6m north, 8m east, 10m vertically upwards.
Consider, east direction to be x-direction, north direction to be y-direction and vertically upward direction to be z-direction.
Displacement of the particle is given by
$\mathop s\limits^ \to = 8\hat i + 6\hat j + 10\hat k$
Magnitude of displacement: $\left| {\vec s} \right| = \sqrt {{6^2} + {8^2} + {{10}^2}} = 10\sqrt 2 m$
So, we need to select the correct option.

Thus, the correct option is A.

Additional Information: Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. The first scientist to measure speed as distance over time was Galileo.

Note: It should always be kept in mind that there is a difference between speed and velocity. Just as distance and displacement have distinctly different meanings, same is the situation between speed and velocity. Velocity is a vector quantity that refers to the rate at which an object changes its position whereas speed is a scalar quantity that refers to how fast an object is moving. Velocity gives us a sense of direction whereas speed does not give any sense of direction. A vector contains two types of information: a magnitude and a direction the direction of a vector is often expressed as an angle of rotation of the vector about its "tail" from east, west, north, or south. The direction of a vector is often expressed as a counter clockwise angle of rotation of the vector about its "tail" from due East.