JEE MAIN - Physics (2019 - 12th April Evening Slot - No. 22)
Two particles are projected from the same point with the same speed u such that they have the same range R,
but different maximum heights, h1 and h2. Which of the following is correct ?
R2
= h1h2
R2
= 16 h1h2
R2
= 4 h1h2
R2 = 2h1h2
Explanation
The range of two particles are same, that means angle of projections must be complementary to each other.
So one angle = $$\theta $$ and other one is = 90o - $$\theta $$
R = $${{{u^2}\sin 2\theta } \over g}$$ = $${{2{u^2}\sin \theta \cos \theta } \over g}$$
$$ \therefore $$ R2 = $${{4{u^4}{{\sin }^2}\theta {{\cos }^2}\theta } \over {{g^2}}}$$
h1 = $${{{u^2}{{\sin }^2}\theta } \over {2g}}$$
h2 = $${{{u^2}{{\sin }^2}\left( {{{90}^o} - \theta } \right)} \over {2g}}$$ = $${{{u^2}{{\cos }^2}\theta } \over {2g}}$$
h1h2 = $${{{u^4}{{\sin }^2}\theta {{\cos }^2}\theta } \over {4{g^2}}}$$
$$ \Rightarrow $$ h1h2 = $${{{R^2}} \over {16}}$$
$$ \Rightarrow $$ R2 = 16 h1h2
So one angle = $$\theta $$ and other one is = 90o - $$\theta $$
R = $${{{u^2}\sin 2\theta } \over g}$$ = $${{2{u^2}\sin \theta \cos \theta } \over g}$$
$$ \therefore $$ R2 = $${{4{u^4}{{\sin }^2}\theta {{\cos }^2}\theta } \over {{g^2}}}$$
h1 = $${{{u^2}{{\sin }^2}\theta } \over {2g}}$$
h2 = $${{{u^2}{{\sin }^2}\left( {{{90}^o} - \theta } \right)} \over {2g}}$$ = $${{{u^2}{{\cos }^2}\theta } \over {2g}}$$
h1h2 = $${{{u^4}{{\sin }^2}\theta {{\cos }^2}\theta } \over {4{g^2}}}$$
$$ \Rightarrow $$ h1h2 = $${{{R^2}} \over {16}}$$
$$ \Rightarrow $$ R2 = 16 h1h2
Comments (0)
