The ranges and heights for two projectiles projected with the sam… - Vidyadip

MCQ

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are ${R}_{1}, {R}_{2}$ and ${H}_{1}$, ${H}_{2}$ respectively. Choose the correct option:

A
${R}_{1}>{R}_{2}$ and ${H}_{1}={H}_{2}$
✓
${R}_{1}={R}_{2}$ and ${H}_{1}<{H}_{2}$
C
${R}_{1}<{R}_{2}$ and ${H}_{1}<{H}_{2}$
D
${R}_{1}={R}_{2}$ and ${H}_{1}={H}_{2}$

✓

Answer

Correct option: B.

${R}_{1}={R}_{2}$ and ${H}_{1}<{H}_{2}$

b
Range ${R}=\frac{{u}^{2} \sin 2 \theta}{{g}}$ and same for $\theta$ and $90-\theta$

So same for $42^{\circ}$ and $48^{\circ}$

Maximum height ${H}=\frac{{u}^{2} \sin ^{2} \theta}{2 {g}}$

${H}$ is high for higher $\theta$

So ${H}$ for $48^{\circ}$ is higher than ${H}$ for $42^{\circ}$

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