Question

Equation of parabolic trajectory of a projectile can be given by:

• A. $\frac{sin\theta }{cos\theta }x-\frac{g{x}^2}{si{n}^2\theta +co{s}^2\theta +cos2\theta }$
• B. $\frac{sin\theta }{cos\theta }x-\frac{g{x}^2}{u^2(si{n}^2\theta +co{s}^2\theta +cos2\theta )}$
• C. $\frac{sin\theta }{cos\theta }x-\frac{g{x}^2}{2u^2(si{n}^2\theta +co{s}^2\theta +cos2\theta )}$
• D. $\frac{sin\theta }{cos\theta }x-\frac{g{x}^2}{u^3(si{n}^2\theta +co{s}^2\theta +cos2\theta )}$

Answer 1

The correct option is B $\frac{sin\theta }{cos\theta }x-\frac{g{x}^2}{u^2(si{n}^2\theta +co{s}^2\theta +cos2\theta )}$

Equation of parabolic trajectory: $y=xtan\theta -\frac{g{x}^2}{2u^{2}co{s}^2\theta }$

Using: $tan\theta =\frac{sin\theta }{cos\theta }$ and $2co{s}^2\theta =1+cos2\theta$

$\therefore$ $y=\frac{sin\theta }{cos\theta }x-\frac{g{x}^2}{u^2[1+cos2\theta ]}$

Now using: $co{s}^2\theta +si{n}^2\theta =1$

$⟹$$y=\frac{sin\theta }{cos\theta }x-\frac{g{x}^2}{u^2[si{n}^2\theta +co{s}^{\theta }+cos2\theta ]}$