A point moves in x-y plane as per x=kt, y = ktleft( {1 - α t} right) where k and

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3-2.Motion in Plane

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A point moves in $x-y$ plane as per $x=kt,$ $y = kt\left( {1 - \alpha t} \right)$ where $k$ and $\alpha \,$ are $+ve$ constants. The equation of trajectory is

A$y = x - \frac{{\alpha {x^2}}}{k}$

B$y = x + \frac{{\alpha {x^2}}}{k}$

C$x = y - \frac{{\alpha {y^2}}}{k}$

D$x = y - \frac{{\alpha {y^2}}}{k}$

Solution

$x=\mathbf{K t}$
$t=\frac{x}{k}$
$y=k t-\alpha k t^{2}$
$y=\frac{k x}{k}-\alpha k\left(\frac{x}{k}\right)^{2}$
$y=x-\frac{\alpha x^{2}}{K}$

Standard 11

Physics

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