Question
Prove that the horizontal range is same when angle of projection is:
  1. Greater than 45° by certain value.
  2. Less than 45° by the same value.

Answer

The horizontal range of the projectile is given by

$\text{R}=\frac{\text{u}^2\sin2\theta}{\text{g}}$

  1. If angle of projection $\theta=45^\circ+\alpha$ and R = R1

then, $\text{R}_1=\frac{\text{u}^2\sin2(45^\circ+\alpha)}{\text{g}}=\frac{\text{u}^2}{\text{g}}\cos2\alpha\dots(\text{i})$

  1. If angle of projection $\theta=45^\circ-\alpha$ and R = R2

$\therefore\ \text{R}_2=\frac{\text{u}^2\sin2(45^\circ-\alpha)}{\text{g}}=\frac{\text{u}^2}{\text{g}}\cos2\alpha\dots(\text{ii})$

Comparing eq. (i) and (ii), we have

R1 = R2

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