If the initial velocity in horizontal direction of a projectile is unit vector i^ and the equation of trajectory is y = 5x(1 – x). The y component vector of the initial velocity is ___ j^.(Take g = 10 m/s2)

y=5x−5x2On comparing withy=xtan⁡θ−12gx2v2tan⁡θ=5=uyux⇒uy=5

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If the initial velocity in horizontal direction of a projectile is 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 m/s²)

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answer is 5.

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Detailed Solution

$\begin{array}{l} y = 5 x - 5 x^{2} \\ On comparing with \\ y = xtan θ - \frac{1}{2} \frac{{gx}^{2}}{v^{2}} \\ \tan θ = 5 = \frac{u_{y}}{u_{x}} \\ \Rightarrow u_{y} = 5 \end{array}$

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