Question

In the given figure for a projectile

Which of the following option is correct?

• A. $y=\left[\frac{x_1{x}_2}{x_1-x_2}\right]\tan \theta$
• B. $y=\left[\frac{x_1{x}_2}{x_1+x_2}\right]\tan \theta$
• C. $y=\left[\frac{2x_1{x}_2}{x_1+x_2}\right]\cos \theta$
• D. $y=\left[\frac{2x_1{x}_2}{x_1+x_2}\right]\tan \theta$

Answer 1

The correct option is B $y=\left[\frac{x_1{x}_2}{x_1+x_2}\right]\tan \theta$

From the figure,

$P=(x_1,y)$
$R=x_1+x_2$
Using equation of trajectory of projectile
$y=x\tan \theta (1-\frac{x}{R})$
$\Rightarrow y=x_1\tan \theta (1-\frac{x_1}{x_1+x_2})$
$y=\tan \theta \left(\frac{x_1{x}_2}{x_1+x_2}\right)$
Hence, the corrext answer is option (b).