QJEEM13Ph5f8a: JEE Main 2013 Physics - Class 11 JEEM13Ph5f8a Solution: A projectile is given an initial velocity of ( i ^ + 2 j ^ )…

Question

Verified Solution • 2025–26 Session moderate

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/s², the equation of its trajectory is:

Accepted Answer

\vec{u} = \hat{i} + 2 \hat{j} = u_{x} \hat{i} + u_{y} \hat{j}

\Rightarrow u \cos θ = 1, u \sin θ = 2

Also

x = u_{x} t

and

y = u_{y} t - \frac{1}{2} g t^{2}

\Rightarrow

y = x \tan θ - \frac{1}{2} \frac{g x^{2}}{u_{x}^{2}}

∴

y = 2 x - \frac{1}{2} g x^{2} = 2 x - 5 x^{2}

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