Question

A projectile is fired with a velocity at right angle $\theta$ to the slope which is inclined at an angle $\theta$ with the horizontal. The expression for the range $R$ along the incline is:

• A. $\frac{2v^2}{g}\sec \theta$
• B. $\frac{2v^2}{g}\tan \theta$
• C. $\frac{2v^2}{g}\sec \theta \tan \theta$
• D. $\frac{2v^2}{g}{\tan }^2\theta$

Answer 1

The correct option is C $\frac{2v^2}{g}\sec \theta \tan \theta$

If 't' is the line of flight, then

$o=vt-\frac{1}{2}gcos\theta t^2$

$t=\frac{2v}{gcos\theta }$

$\Rightarrow R=\frac{1}{2}gsin\theta \times (\frac{2v}{gcos\theta }{)}^2$

$R=\frac{2v^2}{g}tan\theta sec\theta .$