Question 105: Motion in 2D & Vectors

Question

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 ?

Accepted Answer

The range of two particles are same, that means angle of projections must be complementary to each other.
So one angle = $$	heta $$ and other one is = 90
o
- $$	heta $$
R = $${{{u^2}\sin 2	heta } \over g}$$ = $${{2{u^2}\sin 	heta \cos 	heta } \over g}$$
$$ 	herefore $$ R
2
= $${{4{u^4}{{\sin }^2}	heta {{\cos }^2}	heta } \over {{g^2}}}$$
h
1
= $${{{u^2}{{\sin }^2}	heta } \over {2g}}$$
h
2
= $${{{u^2}{{\sin }^2}\left( {{{90}^o} - 	heta } ight)} \over {2g}}$$ = $${{{u^2}{{\cos }^2}	heta } \over {2g}}$$
h
1
h
2
= $${{{u^4}{{\sin }^2}	heta {{\cos }^2}	heta } \over {4{g^2}}}$$
$$ \Rightarrow $$ h
1
h
2
= $${{{R^2}} \over {16}}$$
$$ \Rightarrow $$ R
2
= 16 h
1
h
2

Answer

R2
 = h1h2

Answer

R2
 = 16 h1h2

Answer

R2
 = 4 h1h2

Answer

R2 = 2h1h2

Motion in 2D & Vectors

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 ?

Choose the correct answer: