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Two projectiles are fired from the same point with the same speed at angles of projection $60^o$ and $30^o$ respectively. Which one of the following is true?
Their maximum height will be same
Their range will be same
Their landing velocity will be same
Their time of flight will be same
Solution
$\begin{array}{l}
Given,\,{u_1} = {u_2} = u,\,\,\,\,\,\,{\theta _1} = {60^ \circ },\,\,{\theta _2} = {30^ \circ }\\
In\,1st\,case,\,we\,know\,that\,range\\
{R_1} = \frac{{{u^2}\sin 2\left( {{{60}^ \circ }} \right)}}{g} = \frac{{{u^2}\sin {{120}^ \circ }}}{g}\\
\,\,\,\,\,\,\, = \frac{{{u^2}\sin \left( {{{90}^ \circ } + {{30}^ \circ }} \right)}}{g}\\
= \frac{{{u^2}\left( {\cos {{30}^ \circ }} \right)}}{g} = \frac{{\sqrt 3 {u^2}}}{{2g}}
\end{array}$
$\begin{array}{l}
In\,IInd\,case\,when\,\,{\theta _2} = {30^{ \circ \,}},\,then\\
{R_2} = \frac{{{u^2}\sin {{60}^ \circ }}}{g} = \frac{{{u^2}\sqrt 3 }}{{2g}} \Rightarrow {R_1}{R_2}\\
\left( {we\,get\,same\,value\,of\,ranges} \right).
\end{array}$
