Ratio of Projectile Quantities for Different Launch Parameters
The question asks for the ratio of speeds, heights, or ranges of two projectiles launched with different speeds and/or angles, requiring direct formula comparison rather than complementary-angle symmetry.
Two projectiles are thrown with same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be (1) $1 : \sqrt { 2 }$ (2) $\sqrt { 2 } : 1$ (3) $2 : \sqrt { 3 }$ (4) $\sqrt { 3 } : 2$
A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}$, the ratio of instantaneous velocity to its average velocity is $\pi : x\sqrt{2}$. The value of $x$ will be (1) 2 (2) 5 (3) 1 (4) 7