A cannon elevated at some angle $($unknown$)$ fires a shell with some initial speed $v_0($unknown$)$ that has a range $R$ when fired over level ground $($see Figure $($a$)).$

$($a$)$ No Explosion

During a test fire, a shell explodes at the top of the trajectory into two unequal mass fragments. The shell explodes in such a manner that neither fragment experiences a change in momentum in the $y-$direction. However, $14\%$ of the shell $(m_2)$ continues onward and the other fragment $(m_1)$ falls straight down. Determine the distance $D($in terms of $R)$ that the forward moving fragment lands from the cannon $($see Figure $($b$)).$