A particle projected from origin moves in x-y plane with a velocity vec{v}=3 hat{i}+6 x hat{j} , whe

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3-2.Motion in Plane

hard

A particle projected from origin moves in $x-y$ plane with a velocity $\vec{v}=3 \hat{i}+6 x \hat{j}$, where $\hat{i}$ and $\hat{j}$ are the unit vectors along $x$ and $y$ axis. Find the equation of path followed by the particle

A

$y=x^2$

B

$y=\frac{1}{x^2}$

C

$y=2 x^2$

D

$y=\frac{1}{x}$

Solution

(a)

$v_x \hat{i}+v_y \hat{j}=\vec{V}$

$v_x=3$

$v_y=6 x$

We know

$\frac{d_y}{d_x}=\tan \theta=\frac{V_y}{V_x}$

$\frac{d_y}{d_x}=\frac{6 x}{3 x}$

$\int \limits_0 d y=\int \limits_0{2 x d x}$

$y=x^2$

Standard 11

Physics

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