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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 the 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 C $$y=2x-5x^{2}$$
$$\vec{u} = \hat{i} + 2\hat{j};$$
$$ \therefore u \cos \theta = 1; u \sin \theta =2$$
$$x=u \cos \theta t =t$$
$$y=u \sin \theta t - \dfrac{1}{2}gt^2 = 2t-5t^{2}$$
Substituting $$t=x$$
Equation  of  trajectory  is $$y=2x-5x^{2}$$

Physics

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