Question

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 ______ $\hat{ j }$ (Take $g =10 \,m / s ^2$ )

Answer 1

$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 $
$ \vec{ u }_{ y }=5 \hat{ j }$