The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $\mathrm{R}_1, \mathrm{R}_2$ and $\mathrm{H}_1, \mathrm{H}_2$ respectively. Choose the correct option :
Select the correct option:
A
$\mathrm{R}_1>\mathrm{R}_2$ and $\mathrm{H}_1=\mathrm{H}_2$
B
$\mathrm{R}_1=\mathrm{R}_2$ and $\mathrm{H}_1<\mathrm{H}_2$
C
$\mathrm{R}_1<\mathrm{R}_2$ and $\mathrm{H}_1<\mathrm{H}_2$
D
$\mathrm{R}_1=\mathrm{R}_2$ and $\mathrm{H}_1=\mathrm{H}_2$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Range $\mathrm{R}=\frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{~g}}$ and same for $\theta$ and $90-\theta$
So same for $42^{\circ}$ and $48^{\circ}$
Maximum height $\mathrm{H}=\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}}$
H is high for higher $\theta$
So H for $48^{\circ}$ is higher than H for $42^{\circ}$
Option (2)
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