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Motion in a Plane — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane5 Marks
Question
Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by,
$\theta(\text{t})=\tan^{-1}\Big(\frac{\text{u}_\text{oy}-\text{gt}}{\text{u}_\text{ox}}\Big)$
✓

Answer

Let vox and v0y respectively be the initial components of the velocity of the projectile along horizontal (x) and vertical (y) directions.
Let vx and vy respectively be the horizontal and vertical components of velocity at a point P.

Time taken by the projectile to reach point P = t
Applying the first equation of motion along the vertical and horizontal directions, we get:
vy = voy = gt
And vx = vox
$\therefore\tan\theta=\frac{\text{v}_\text{y}}{\text{v}_\text{x}}=\frac{\text{v}_\text{oy}-\text{gt}}{\text{v}_\text{ox}}$
$\theta=\frac{\tan^{-1}(\text{v}_\text{oy}-\text{gt})}{\text{v}_\text{ox}}$

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