If the initial velocity in horizontal direction of a projectile is unit vector hati 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 )

Question

If the initial velocity in horizontal direction of a projectile is unit vector hati 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 ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

ux=1 y=5 x(1-x) (d y/d t)=5 (d x/d t)-10 x (d x/d t) For initial y-component of velocity u y =(( dy / dt )) x =0 ⇒ 5(1)=5 vec u y =5 hat j

Q. 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 $g = 10 m / s^{2}$ )

$u_{x} = 1$
$y = 5 x (1 - x)$
$\frac{d y}{d t} = 5 \frac{d x}{d t} - 10 x \frac{d x}{d t}$
For initial y-component of velocity
$u_{y} = (\frac{d y}{d t})_{x = 0} \Rightarrow 5 (1) = 5$
$u_{y} = 5 \hat{j}$

Q. 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=10m/s2 )

ux​=1 y=5x(1−x) dtdy​=5dtdx​−10xdtdx​ For initial y-component of velocity uy​=(dtdy​)x=0​⇒5(1)=5 uy​=5j^​

Q. 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 $g = 10 m / s^{2}$ )

$u_{x} = 1$
$y = 5 x (1 - x)$
$\frac{d y}{d t} = 5 \frac{d x}{d t} - 10 x \frac{d x}{d t}$
For initial y-component of velocity
$u_{y} = (\frac{d y}{d t})_{x = 0} \Rightarrow 5 (1) = 5$
$u_{y} = 5 \hat{j}$