A projectile is fired at an angle of 45^o&nbs | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\begin{array}{l}
Let\,\phi \,be\,elevation\,angle\,of\,the\,projectile\
at\,its\,highest\,{m{point}}\,{m{as}}\,{m{seen}}\,{m{from}}\,{m{

Vedclass · Accepted Answer

$ta{n^{ - 1}}\left( {\frac{1}{2}} \right)$

Vedclass · Answer

$\begin{array}{l}
Let\,\phi \,be\,elevation\,angle\,of\,the\,projectile\
at\,its\,highest\,{m{point}}\,{m{as}}\,{m{seen}}\,{m{from}}\,{m{the}}\
{m{ point}}\,of\,projection\,O\,and\,	heta \,be\,angle\,of\
projection\,with\,the\,horizontal.\
From\,figure,\,	an \phi  = \frac{H}{{R/2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i ight)\
In\,case\,of\,projectile\,motion\
Maximum\,height,\,H = \frac{{{h^2}{{\sin }^2}2	heta }}{{2g}}\
Horizontal\,range,R = \frac{{{h^2}\sin 2	heta }}{g}\
Substituting\,theses\,values\,of\,H\,and\,R\
in\,\left( i ight),\,we\,get
\end{array}$

$\begin{array}{l}
\,\,\,\,\,\,\,\,\,	an \phi  = \frac{{\frac{{{u^2}{{\sin }^2}	heta }}{{2g}}}}{{\frac{{{u^2}\sin 	heta }}{{2g}}}}\
\,\,\,\,\,\,\,\,\,\,	an \phi  = \frac{{{{\sin }^2}	heta }}{{\sin 2	heta }} = \frac{{{{\sin }^2}	heta }}{{2\sin 	heta \cos 	heta }} = \frac{1}{2}	an 	heta \
\,\,\,\,	an \phi  = \frac{1}{2}	an {45^ \circ } = \frac{1}{2}\
Here,	heta  = {45^ \circ }\
	herefore \,\,\,\,\,	an \phi  = \frac{1}{2}	an {45^ \circ } = \frac{1}{2}\,\,\,\,\left( {\,	an \,{{45}^ \circ } = 1} ight)\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\phi  = {	an ^{ - 1}}\left( {\frac{1}{2}} ight)
\end{array}$

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 projectile is fired at an angle of $45^o $ with the horizontal . Elevation angle of the projectile at its highest point as seen from the point of projection, is

Similar Questions

A ball is projected upwards from the top of tower with a velocity $50\,\,m{s^{ - 1}}$ making an angle ${30^o}$ with the horizontal. The height of tower is $ 70 \,m$. After how many seconds from the instant of throwing will the ball reach the ground ........ $\sec$

A body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of ${30^o}$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$

A cricketer can throw a ball to a maximum horizontal distance of $100 \,m$. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is ......... $m$