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Question

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


A
y=x5x2
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B
y=2x5x2
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C
y=2x15x2
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D
y=2x25x2
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Solution

The correct option is C $$y = 2x - 5x^{2}$$
Given, $$\vec {u} = \hat {i} + 2\hat {j} = u_{x}\hat {i} + u_{y}\hat {j}$$
Then, $$u_{x} = 1 = u\cos \theta$$
and $$u_{y} = 2 = u\sin \theta$$
$$\therefore \tan \theta = \dfrac {u\sin \theta}{u\cos \theta} = \dfrac {2}{1} = 2$$
The equation of trajectory of a projectile motion is
$$y = x\tan \theta - \dfrac {gx^{2}}{2u^{2} \cos^{2} \theta} = x\tan \theta - \dfrac {gx^{2}}{2(u\cos \theta)^{2}}$$
$$\therefore y = x \times 2 - \dfrac {10\times x^{2}}{2(1)^{2}} = 2x - 5x^{2}$$.

Physics

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