Question

A projectile fires with velocity u at right angle to the slope which is inclined at an angle $\theta$ with horizontal. the expressioin for R is

Answer 1

If 't' is the time of flight, then

$S=ut+\frac{1}{2}(-g\cos \theta )t^2$

$0=ut-\frac{1}{2}g\cos \theta t^2$

$ut=\frac{1}{2}g\cos \theta t^2$

$t=\frac{2u}{g\cos \theta }$

Then,

$R=\frac{1}{2}g\sin \theta \times {\left(\frac{2u}{g\cos \theta }\right)}^2$

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