$\vec{v}=a i+(b-c i) j$ $\Rightarrow \quad v_{x}=a \quad v_{y}=b-c t$ $a_{y}=\frac{d v_{y}}{d t}=-c$ $R=\frac{2 u_{x} u_{y}}{a_{y}} \Rightarr

$\vec{v}=a i+(b-c i) j$ $\Rightarrow \quad v_{x}=a \quad v_{y}=b-c t$ $a_{y}=\frac{d v_{y}}{d t}=-c$ $R=\frac{2 u_{x} u_{y}}{a_{y}} \Rightarrow R=\frac{2 a b}{c}$

English

3-2.Motion in PlaneDifficult

A particle is projected from a horizontal plane ($x-z$ plane) such that its velocity vector at time t is given by $\vec V = a\hat i + (b - ct)\hat j$ Its range on the horizontal plane is given by

A
$\frac{{ba}}{c}$
B
$\frac{{2ba}}{c}$
C
$\frac{{3ba}}{c}$
D
None

Std 11
Physics

Column $-I$

Angle of projection
Column $-II$

$A.$ $\theta \, = \,{45^o}$ $1.$ $\frac{{{K_h}}}{{{K_i}}} = \frac{1}{4}$

$B.$ $\theta \, = \,{60^o}$ $2.$ $\frac{{g{T^2}}}{R} = 8$

$C.$ $\theta \, = \,{30^o}$ $3.$ $\frac{R}{H} = 4\sqrt 3 $

$D.$ $\theta \, = \,{\tan ^{ - 1}}\,4$ $4.$ $\frac{R}{H} = 4$

$K_i :$ initial kinetic energy

$K_h :$ kinetic energy at the highest point

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[JEE MAIN 2022]

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A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m / s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\frac{m}{s}$

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Column $-I$ Angle of projection	Column $-II$
$A.$ $\theta \, = \,{45^o}$	$1.$ $\frac{{{K_h}}}{{{K_i}}} = \frac{1}{4}$
$B.$ $\theta \, = \,{60^o}$	$2.$ $\frac{{g{T^2}}}{R} = 8$
$C.$ $\theta \, = \,{30^o}$	$3.$ $\frac{R}{H} = 4\sqrt 3 $
$D.$ $\theta \, = \,{\tan ^{ - 1}}\,4$	$4.$ $\frac{R}{H} = 4$

A particle is projected from a horizontal plane ($x-z$ plane) such that its velocity vector at time t is given by $\vec V = a\hat i + (b - ct)\hat j$ Its range on the horizontal plane is given by

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