Question

Two projectiles A and B are projected with angle of projection 15° for the projectile A and 45° for the projectile B. If RA and RB be the horizontal range for the two projectiles, then
(a) RA < RB
(b) RA > RB
(c) RA = RB
(d) the information is insufficient to decide the relation of RA with RB.

Answer 1

Answer:optind

Explanation:

Answer 2

If $R_A$ and $R_B$ be the horizontal range for the two projectiles, then the information is insufficient to decide the relation of $R_A$ with $R_B$.

Option (d) the information is insufficient to decide the relation of $R_A$with $R_B$.

Explanation:  

Horizontal range for the projectile,

                                               $\mathrm{R}=\frac{u^{2} \sin 2 \theta}{g}$        

Here,    u = projected velocity

            g = gravity

When,  

Angle of projection is  θ = 15°

            $R=\frac{u^{2} \sin 2 \times 15}{g}$

             $\mathrm{R}=\frac{u^{2} \sin 30}{g}$

When,

Angle of projection is  θ = 45°

           $R=\frac{u^{2} \sin 2 \times 45}{g}$

           $\mathrm{R}=\frac{u^{2} \sin 90}{g}$

( u = projected velocity is not given )

The range of a projectile depends upon the projected velocity and the angle of projection (θ ) as is clear from the formula $R=\frac{u^{2} \sin 2 \theta}{g}$ .

But in this question the projected velocity is not given , only angle of projection is given .

Therefore, the information is not sufficient to decide the relation of $R_A$ with $R_B$.