Physics - Kinematics Question with Solution | TestHub

Taking initial and final velocities on x and y axis. $0=\mathrm{u}-\mathrm{g}\sin \alpha \mathrm{t}$ $\mathrm{t}=\frac{\mathrm{u}}{\mathrm{g}{\sin }^2}$

$\mathrm{x}=\mathrm{u}\left[\frac{\mathrm{u}}{\mathrm{g}{\sin }^2}\right]-\frac{1}{2}(\mathrm{g}\sin \alpha ){\left[\frac{\mathrm{u}}{\left(\mathrm{g}{\sin }^2\right)}\right]}^2=\frac{{\mathrm{u}}^2}{2\mathrm{g}\sin \alpha }$

$y=\frac{1}{2}g\cos a{\left[\frac{u}{g\sin \alpha }\right]}^2=\frac{u^2}{2g}\left(\frac{\cos \alpha }{{\sin }^2\alpha }\right)$

$\mathrm{OP}=\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2}=\frac{{\mathrm{u}}^2}{2\mathrm{g}\sin \alpha }$

$\tan \varphi =\frac{\mathrm{y}}{\mathrm{x}}=\frac{\cos \alpha \times \sin \alpha }{{\sin }^2\alpha }=\cot \alpha$

$\mathrm{v}=0+\mathrm{g}\cos \mathrm{a}\left[\frac{\mathrm{u}}{\mathrm{g}\sin \alpha }\right]=\mathrm{u}\cot \alpha$