Five balls A,B,C,D and E are projected with the same speed making angles of 10^o, 30^o, 45^o, 60^o and 80^o respectively with the horizontal. Which ball will strike the ground at the farthest point?

The horizontal range of a projectile is given by

$\mathrm{R}=\frac{{\mathrm{u}}^2\sin 2\mathrm{\theta }}{\mathrm{g}}$

The range R is maximum when $\sin 2\mathrm{\theta }$ is maximum. Thus

$\sin 2\mathrm{\theta }=1\text{ or }2\mathrm{\theta }=\mathrm{\pi }/2$

or               $\mathrm{\theta }=\mathrm{\pi }/4$

$\therefore \mathrm{\theta }={45}^{\circ }$

So, the body C will have the maximum range.