Question

Two particles A and B are projected with same speed so that the ratio of their maximum height reached is 3: 1 . If the speed of A is doubled without altering other parameters, the ratio of the horizontal ranges attained by A and B is

• A. 1: 1
• B. 2: 1
• C. 4: 1
• D. 3: 2

Answer 1

Answer: (C)

Given, $\frac{H_1}{H_2}=\frac{3}{1}$
$\therefore H_1=3H_2$
or $\frac{u^2{\sin }^2{\theta }_1}{2g}=\frac{3u^2{\sin }^2{\theta }_2}{2g}$
or $\frac{{\sin }^2{\theta }_1}{{\sin }^2{\theta }_2}=\frac{3}{1}$
It is true if ${\theta }_1=60^{\circ }$ and ${\theta }_2=30^{\circ }$
When speed of $A$ is doubled, then horizontal range
$R_1=\frac{(2u{)}^2\sin \left(2\times 60^{\circ }\right)}{g}$
$=\frac{4u^2\sin 120^{\circ }}{g}$
$=\frac{4u^2\sin 60^{\circ }}{g}$
and $R_2=\frac{u^2\sin \left(2\times 30^{\circ }\right)}{g}$
$=\frac{u^2\sin 60^{\circ }}{g}$
$\therefore \frac{R_1}{R_2}=\frac{4}{1}$