The two projectiles are projected with the same initial velocities at and with respect to the horizontal

Question

The two projectiles are projected with the same initial velocities at $15 °$ and $30 °$ with respect to the horizontal. The ratio of their ranges is $1 : x$ . The value of $x$ is [2026]

Smart Achievers · Accepted Answer

(2)

$R \propto \sin (2 θ)$

$x$

Solution

Q.
The two projectiles are projected with the same initial velocities at $15 °$ and $30 °$ with respect to the horizontal. The ratio of their ranges is $1 : x$ . The value of $x$ is [2026]

1 $\sqrt{2}$

2 $\sqrt{3}$

3 $2 \sqrt{3}$

4 $\frac{1}{\sqrt{2}}$

Ans.
(2)

$R \propto \sin (2 θ)$

$\frac{R_{1}}{R_{2}} = \frac{\sin (2 \times 15 °)}{\sin (2 \times 30 °)} = \frac{1 / 2}{\sqrt{3} / 2} = \frac{1}{\sqrt{3}}$

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Solution

Q. The two projectiles are projected with the same initial velocities at 15° and 30° with respect to the horizontal. The ratio of their ranges is 1:x. The value of x is [2026]

1 2

2 3

3 23

4 12

Ans. (2) R∝sin(2θ) R1R2=sin(2×15°)sin(2×30°)=1/23/2=13