The velocity of a particle having a magnitude | vedclass

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Question

(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

Vedclass · Accepted Answer

$5 \hat{i}+5 \sqrt{3} \hat{j}$

Vedclass · Answer

(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 $	heta = 60^{\circ}$.The components are given by:$v_x = v \cos 	heta = 10 \cos 60^{\circ} = 10 	imes \frac{1}{2} = 5 \ m/s$$v_y = v \sin 	heta = 10 \sin 60^{\circ} = 10 	imes \frac{\sqrt{3}}{2} = 5 \sqrt{3} \ m/s$Thus,the velocity vector is $\vec{v} = v_x \hat{i} + v_y \hat{j} = 5 \hat{i} + 5 \sqrt{3} \hat{j} \ m/s$.

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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