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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
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B
9y=12x5x2
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C
y=0x5x2
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D
5y=x9x2
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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,

$$y=2x-\dfrac 12 \dfrac{10x^2}{(1^2+2^2)\times \dfrac{1}{1+tan\,\theta}}=2x-\dfrac 12 \dfrac{10x^2}{(1^2+2^2)\times \dfrac 15}$$

$$\implies y=2x-5x^2$$

1432335_1077409_ans_052f7afd32444ca194c5b3601be7da0b.PNG

Physics

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