Question

An aircraft moves $400m$ towards north $300m$ towards west and then $1200m$ vertically upward then its displacement from the initial position is

• A. $1500m$
• B. $1400m$
• C. $1300m$
• D. $1200m$

Answer 1

The correct option is C

$1300m$

Step 1: Given

Displacement along north direction: $\overrightarrow{d_N}=400\hat{i}$

Displacement along west direction: $\overrightarrow{d_W}=300\hat{j}$

Displacement upwards: $\overrightarrow{d_U}=1200\hat{k}$

Step 2: Formula Used

$\overrightarrow{\left|d\right|}=\sqrt{{d_1}^2+{d_2}^2}$

Step 3: Find the total displacement

Calculate the displacement as the plane first moves in North and then in West.

$$\begin{gathered} \overrightarrow{\left|d_{NW}\right|}=\sqrt{{400}^2+{300}^2} \\ =\sqrt{160000+90000} \\ =\sqrt{250000} \\ =500m \end{gathered}$$

Calculate the displacement as the plane first moves in North-West direction an then upwards. Use the displacement in North-West direction obtained, $500m$.

$$\begin{gathered} \overrightarrow{\left|d\right|}=\sqrt{{500}^2+{1200}^2} \\ =\sqrt{250000+1440000} \\ =\sqrt{1690000} \\ =1300m \end{gathered}$$

Hence, the total displacement is $1300m$.