A projectile is launched at a speed u and an angle heta above a...

The horizontal range of the projectile before the first collision is $R_1 = \dfrac{u^2 \sin 2\theta}{g}$.

At the first collision, the horizontal component of velocity $u \cos \theta$ remains unchanged, while the vertical component of velocity becomes $e u \sin \theta$ directed upwards.

The time of flight for the motion between the first and second collision is $T_2 = \dfrac{2(e u \sin \theta)}{g}$.

The horizontal distance covered between the first and second collision is $R_2 = (u \cos \theta) T_2 = \dfrac{2 e u^2 \sin \theta \cos \theta}{g} = \dfrac{e u^2 \sin 2\theta}{g}$.

The total distance from the launch point to the second collision is $R = R_1 + R_2 = \dfrac{u^2 \sin 2\theta}{g} + \dfrac{e u^2 \sin 2\theta}{g} = \dfrac{(1 + e)u^2 \sin 2\theta}{g}$.