(A) Let the total distance covered be $d = 500 \,m$ at an angle $\theta = 60^o$ with the horizontal runway.The horizontal component of the distance is

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Horizontal: $250 \,m$,Vertical: $250 \sqrt{3} \,m$

(A) Let the total distance covered be $d = 500 \,m$ at an angle $\theta = 60^o$ with the horizontal runway.The horizontal component of the distance is given by $d_x = d \cos(\theta)$.$d_x = 500 \cos(60^o) = 500 \times (1/2) = 250 \,m$.The vertical component of the distance is given by $d_y = d \sin(\theta)$.$d_y = 500 \sin(60^o) = 500 \times (\sqrt{3}/2) = 250 \sqrt{3} \,m$.Therefore,the horizontal distance is $250 \,m$ and the vertical distance is $250 \sqrt{3} \,m$.

Class 11 Physics 3-1.Vectors Resolution of a Vector into Rectangular Components

Medium

$A$ plane covers $500 \,m$ in a direction $60^o$ with the runway while starting the flight. Find the distance covered by the plane in the horizontal and vertical directions.

A
Horizontal: $250 \,m$,Vertical: $250 \sqrt{3} \,m$
B
Horizontal: $250 \sqrt{3} \,m$,Vertical: $250 \,m$
C
Horizontal: $500 \,m$,Vertical: $0 \,m$
D
Horizontal: $0 \,m$,Vertical: $500 \,m$

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Resolution of a Vector into Rectangular Components

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$A$ plane covers $500 \,m$ in a direction $60^o$ with the runway while starting the flight. Find the distance covered by the plane in the horizontal and vertical directions.

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What is the maximum number of components a vector can have when resolved in a plane?

Vector $P = 6 \hat{i} + 4 \sqrt{2} \hat{j} + 4 \sqrt{2} \hat{k}$ makes an angle with the $z$-axis equal to:

The resultant of these forces $\overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately $\ldots \ldots \text{N}$.[Take $\sqrt{3}=1.7, \sqrt{2}=1.4$. Given $\hat{i}$ and $\hat{j}$ are unit vectors along $x, y$ axes.]

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The resultant of these forces $\overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately $\ldots \ldots \text{N}$.
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