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JEE Main 2022 (26 Jul, Shift 1) · Projectile Basics & Trajectory

Projectile Basics & Trajectory question from JEE Main 2022 (26 Jul, Shift 1)

Q3JEE Main 2022 · 26 JUL · SHIFT 1Medium

Projectile Basics & Trajectory

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

Numerical answer type. Work it out, then open the answer.

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Answer: 5

$y = 5x - 5x^2$ ; compare with $y = x\frac{u_y}{u_x} - \frac{gx^2}{2u_x^2}$
$\frac{g}{2u_x^2} = \frac{10}{2(1)^2} = 5$ (consistent with $u_x = 1$ )
$\frac{u_y}{u_x} = 5 \Rightarrow u_y = 5$
So the $y$ component is $5\hat j$ m/s, answer 5.

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