Question

An airplane flies $400m$ north and $300m$ south and then flies $1200m$ upwards then net displacement is:

• A. $1400m$
• B. $1204.15m$
• C. $1300m$
• D. $1500.15m$

Answer 1

The correct option is B

$1204.15m$

Step 1: Given

Distance travelled in North: $D_1=400m$

Distance travelled in the South: $D_2=300m$

Distance travelled Upwards: $D_3=1200m$

The motion of the plane could be better understood by the following diagram:

Step 2: Formula Used

$hypotenus{e}^2=perpendicula{r}^2+bas{e}^2$

Step 3: Calculate the displacement of the plane

Calculate the distance from point A to point C by subtracting the distance of CB from AB

$$\begin{gathered} AC=AB-CB \\ =D_1-D_2 \\ =400m-300m \\ =100m \end{gathered}$$

Calculate the distance from point A to point D using the hypotenuse theorem

$$\begin{gathered} A{D}^2=A{C}^2+C{D}^2 \\ \Rightarrow AD=\sqrt{A{C}^2+C{D}^2} \\ =\sqrt{{100}^2+{1200}^2} \\ =\sqrt{145000} \\ =1204.15 \end{gathered}$$

Hence, the net displacement is $1204.15m$.

Thus, option (B) is correct.