If initial velocity in horizontal direction of a projectile is unit vector hat{i} and equation of tr

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3-2.Motion in Plane

medium

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

A$4$

B$3$

C$5$

D$80$

(JEE MAIN-2022)

Solution

$u_{x}=1$
$y=5 x(1-x)$
$\frac{d y}{d t}=5 \frac{d x}{d t}-10 x \frac{d x}{d t}$
For initial $y$-component of velocity
$u _{ y }=\left(\frac{ dy }{ dt }\right)_{ x =0} \Rightarrow 5(1)=5$
$\overrightarrow{ u }_{ y }=5\,\hat{j }$

Standard 11

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(AIPMT-2013)

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