Velocity horizontal direction |ProjectileMotionJEEMain2022

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JEE MAIN 2022

26-07-2022 S1

Question

If the initial velocity in horizontal direction of a projectile is unit vector $\hat{\mathrm{i}}$ and the equation of trajectory is y = 5x (1 – x). The y component vector of the initial velocity is _____ $\hat{\mathrm{j}}\left(\right.$ Take $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

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Solution

$$ \begin{aligned} & u_x=1 \\ & y=5 x(1-x) \\ & \frac{d y}{d t}=5 \frac{d x}{d t}-10 x \frac{d x}{d t} \end{aligned} $$ For initial y-component of velocity $$ \begin{aligned} & u_y=\left(\frac{d y}{d t}\right)_{x=0} \Rightarrow 5(1)=5 \\ & \vec{u}_y=5 \hat{j} \end{aligned} $$

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