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Question

A projectile is given an initial velocity of $$(\hat {i} + 2\hat {j})m/s$$, where $$\hat {i}$$ is along ground and $$\hat {j}$$ is along the vertical. If $$g = 10\ m/s^{2}$$, the equation of its trajectory is


A
y=2x5x2
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B
4y=2x5x2
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C
4y=2x25x2
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D
y=x5x2
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Solution

The correct option is D $$y =2x - 5x^{2}$$
The equation of projectile is given by,
$$Y=xtan\theta-\dfrac{gx^2}{2u^2cos^2\theta}$$
$$tan\theta=\dfrac{u_{y}}u_{x}=\frac{2}{1}=2$$
$$\Rightarrow y=2x-\frac{1}{2}\dfrac{10x^2}{(1^2+2^2)\times\dfrac{1}{5}}$$
$$\Rightarrow y=2x-5x^2$$
Hence the correct option is A

Physics

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