Find the equation of the particle's trajectory $y (x)$ .

y (x) = (\frac{b}{2 a}) x^{2}

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y (x) = (\frac{a}{2 b}) x^{2}

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y (x) = (\frac{2 b}{a}) x^{2}

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y (x) = (\frac{2 a}{b}) x^{2}

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Solution

The correct option is A $y (x) = (\frac{b}{2 a}) x^{2}$
$v_{x} = a s o, x = a t$ (Using $s = u t + \frac{1}{2} a t^{2}$ )
$v_{y} = b x = a b t$
Again using $s = u t + \frac{1}{2} a t^{2}$
$v_{y} = \frac{d y}{d t} = a b t$
or
$y = \frac{a b t^{2}}{2} = \frac{b x^{2}}{2 a}$ by integration

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