Question

A projectile is fired with a velocity u at right angles to the slope, which is inclined at an angle $\theta$ with the horizontal. Derive an expression for the distance R to the point of impact.

• A. $\frac{2V^{2}tan\theta }{gcos\theta }$
• B. $\frac{2V^{2}tan\theta }{g}$
• C. $\frac{2V^{2}cot\theta }{gcos\theta }$
• D. $\frac{2V^{2}tan\theta }{gsin\theta }$

Answer 1

The correct option is A $\frac{2V^{2}tan\theta }{gcos\theta }$

$u_x=0,a_x=gsin\theta u_y=u,a_y=-gcos\theta Y=0=u_{y}t+\frac{1}{2}{a}_y{t}^2\Rightarrow T=\frac{2u_y}{{-a}_y}=\frac{2u}{gcos\theta }R=u_{x}T+\frac{1}{2}{a}_x{T}^2=\frac{1}{2}gsin\theta {\left(\frac{2u}{gcos\theta }\right)}^2=\frac{2u^{2}tan\theta }{gcos\theta }$