The range of a projectile at an angle $\theta$ is equal to half of the maximum range if thrown at the same speed. The angle of projection $\theta$ is given by :

for a projectile thrown up an incline plane (making an angle $\theta$ with
horiontal), maximum range on the incline
can be achieved by projecting at an angle .. from the horizontal ( $\theta$ is acute).

A projectile thrown with an initial speed u and angle of projection ${15}^{\circ }$ to the horizontal has a range R. If the same projectile is thrown at an angle of ${45}^{\circ }$ to the horizontal with speed 2u, its range will be