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3-2.Motion in Plane
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Two particles $A$ and $B$ are moving in $XY$ plane. Particle $A$ moves along a line with equation $y = x$ while $B$ moves along $X$ axis such that their $X$ coordinates are always equal. If $B$ moves with a uniform speed $3\ m/s$ , the speed of $A$ is
A
$3\ m/s$
B
$\frac {1}{3}\ m/s $
C
$3\sqrt 2 \ m/s$
D
$\frac {3}{\sqrt 2}\ m/s$
Solution
For particle $A$
$y=x$
$\frac{d y}{d t}=\frac{d x}{d t} \Rightarrow v_{y_{A}}=v_{x_{A}}$
$\ v_{B}=3 \hat{i}$
$\ \mathrm{v}_{\mathrm{x}_{\mathrm{A}}}=\mathrm{v}_{\mathrm{B}}$
$\Rightarrow \mathrm{v}_{\mathrm{x}_{\mathrm{A}}}=3 \hat{\mathrm{i}} \Rightarrow \mathrm{v}_{\mathrm{y}_{\mathrm{A}}}=3 \hat{\mathrm{j}}$
$\Rightarrow \vec{v}_{A}=3 \hat{i}+3 \hat{j} \Rightarrow\left|\vec{v}_{A}\right|=3 \sqrt{2} \mathrm{m} / \mathrm{s}$
Standard 11
Physics
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