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Motion in a Plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane2 Marks
Question
Prove that the horizontal range is same when angle of projection is:
  1. Greater than $45^\circ$ by certain value.
  2. Less than $45^\circ$ 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 $R = R_1$
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 $R = R_2$
$\therefore\ \text{R}_2=\frac{\text{u}^2\sin2(45^\circ-\alpha)}{\text{g}}=\frac{\text{u}^2}{\text{g}}\cos2\alpha\dots(\text{ii})$
Comparing eq. $(i)$ and $(ii),$ we have $R_1$ = $R_2$

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