Question

# A projectile is given an initial velocity $$\hat { i } +2\hat { j }$$. The Cartesian equation of its path is ($$g=10 ms^-2$$)

A
y=2x5x2
B
9y=12x5x2
C
y=0x5x2
D
5y=x9x2

Solution

## The correct option is A $$y=2x-5x^2$$The equation of projectile is given by$$y=x\,tan\,\theta - \dfrac 12 \dfrac {gx^2}{u^2\,cos^2\theta}$$Here,$$tan\, \theta=\dfrac{U_y}{U_x}=\dfrac 21=2$$Therefore,$$y=2x-\dfrac 12 \dfrac{10x^2}{(1^2+2^2)\times \dfrac{1}{1+tan\,\theta}}=2x-\dfrac 12 \dfrac{10x^2}{(1^2+2^2)\times \dfrac 15}$$$$\implies y=2x-5x^2$$Physics

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