Question

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 $H _{1}= H _{2}$
• B. $R _{1}= R _{2}$ 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 1

Answer: (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 $42^{\circ}$