(D) The velocity vector $\vec{v}$ can be resolved into its rectangular components along the $X$ and $Y$ axes.Given magnitude $v = 10 \ m/s$ and angle

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(D) The velocity vector $\vec{v}$ can be resolved into its rectangular components along the $X$ and $Y$ axes.Given magnitude $v = 10 \ m/s$ and angle $\theta = 60^{\circ}$.The components are given by:$v_x = v \cos \theta = 10 \cos 60^{\circ} = 10 \times \frac{1}{2} = 5 \ m/s$$v_y = v \sin \theta = 10 \sin 60^{\circ} = 10 \times \frac{\sqrt{3}}{2} = 5 \sqrt{3} \ m/s$Thus, the velocity vector is $\vec{v} = v_x \hat{i} + v_y \hat{j} = 5 \hat{i} + 5 \sqrt{3} \hat{j} \ m/s$.

Class 11 Physics 1 Motion in a Plane: Vectors Resolution of a Vector into Rectangular Components

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The velocity of a particle having a magnitude of $10 \ m/s$ in the direction of $60^{\circ}$ with the positive $X$-axis is:

TS EAMCET 2023 All TS EAMCET

A
$5 \hat{i}-5 \sqrt{3} \hat{j}$
B
$5 \sqrt{3} \hat{i}-5 \hat{j}$
C
$5 \sqrt{3} \hat{i}+5 \hat{j}$
D
$5 \hat{i}+5 \sqrt{3} \hat{j}$

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1 Motion in a Plane: Vectors

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Resolution of a Vector into Rectangular Components

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The velocity of a particle having a magnitude of $10 \ m/s$ in the direction of $60^{\circ}$ with the positive $X$-axis is:

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