QJEEM22Ph65c4: JEE Main 2022 Physics - Class 11 JEEM22Ph65c4 Solution: If the initial velocity in horizontal direction of a projectile …

If the initial velocity in the horizontal direction of a projectile is represented by the unit vector $\hat{i}$ and the equation of the trajectory is given by $y = 5x(1 - x)$ , we need to find the $y$ component vector of the initial velocity. (Given: $g = 10 \mathrm{\ m/s^2}$ )

The trajectory equation can be expanded as:

$y = 5x - 5x^2$

In the general form of a projectile's trajectory: $y = x \tan \theta - \frac{1}{2} \frac{g x^2}{v_0^2}$

Here, the equation compares as follows:

$\tan \theta = 5 = \frac{u_y}{u_x}$

Given that the initial horizontal velocity component, $u_x$ , is 1 (unit vector $\hat{i}$ ), we can find $u_y$ from the relationship:

$u_y = 5 \times 1 = 5$

Therefore, the $y$ component vector of the initial velocity is 5 $\hat{j}$ .