Question

A projectile is fired with a velocity $v$ at right angle to the slope which is inclined at an angle $\theta$ with the horizontal. The range of the projectile along the inclined plane is:

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

Answer 1

Answer: (C)

If $t$ is the time of flight, then
$0=v t-\frac{1}{2}(g \cos \theta) t^2 $
$\Rightarrow t=\frac{2 v}{g} g \cos \theta$
$R=0+\frac{1}{2}(g \sin \theta) t^2=\frac{1}{2} g \sin \theta\left(\frac{2 v}{g \cos \theta}\right)^2$
$=\frac{2 v^2}{g} \tan \theta \sec \theta$