Motion in a Plane — Physics STD 11 Science — Question
Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane2 Marks
Question
Prove the following statement "For Elevations which exceed or fall short of 45° by equal amounts, the ranges are equal”.
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Answer
Case I: When angle of projection $\theta=45^\circ+\alpha$ Range, $\text{R}_1=\frac{\text{u}^2\sin2(45^\circ+\alpha)}{\text{g}}$ $=\frac{\text{u}^2\cos2\alpha}{\text{g}}$ Case II: When angle of projection $\theta=45^\circ-\alpha$ Range, $\text{R}_2=\frac{\text{u}^2\sin2(45^\circ-\alpha)}{\text{g}}$ $=\frac{\text{u}^2}{\text{g}}\sin(90^\circ-2\alpha)$ $=\frac{\text{u}^2\cos2\alpha}{\text{g}}=\text{R}_1$
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