Question

An inclined plane makes an angle ${\theta }_0={30}^o$ with the horizontal. A particle is projected from this plane with a speed of $5m{s}^{-1}$ at an angle of elevation $\beta ={30}^o$ with the horizontal as shown in Fig.
a. Find the range of the particle on the plane when it strikes the plane.
b. find the range of the particle for $\beta =120$

Answer 1

a. ${\alpha }^{\prime }={\theta }_0+\beta ={60}^o$
$R=\frac{u^2}{gcos{\theta }_0}\left[sin\right(2{\alpha }^{\prime }-{\theta }_0)+sin{\theta }_0]$
$=\frac{5^2}{10co{s}^2{30}^o}\left[sin\right(2\times {60}^o-{30}^o)+sin{30}^o]=5m$
b. $\alpha +{\theta }_0+{120}^o={180}^o\Rightarrow \alpha ={30}^o$
$R=\frac{u^2}{gcos{\theta }_0}\left[sin\right(2\alpha +{\theta }_0)-sin{\theta }_0]$
$=\frac{5^2}{10co{s}^2{30}^o}\left[sin\right(2\times {30}^o+{30}^o)-sin{30}^o]=5/3m$