Q 11-03-116JEE MainJEE Main 2022 (26 Jul, Shift 1)Easy
If the initial velocity in the horizontal direction of a projectile is the unit vector $\hat i$ and the equation of trajectory is $y = 5x(1 - x)$, the $y$ component vector of the initial velocity is ______ $\hat j$. (Take $g = 10\ \text{m s}^{-2}$)
Numerical value type. Enter your answer.
Answer: 5
Compare with $y = x\tan\theta - \dfrac{gx^2}{2u_x^2}$: $y = 5x - 5x^2$ gives $\tan\theta = \dfrac{u_y}{u_x} = 5$.
With $u_x = 1\ \text{m s}^{-1}$ (check: $\dfrac{g}{2u_x^2} = 5$ ✓), $u_y = 5$, so the answer is $5\hat j$.
Solution by Sreeraj P, M.Sc Physics