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

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 APhysics

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