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

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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