A mortar fires a shell of mass m at speed v₀. The shell explodes at the top of its trajectory (shown by a star in (Figure 1)) as

Question

A mortar fires a shell of mass m at speed v₀. The shell explodes at the top of its trajectory (shown by a star in (Figure 1)) as designed. However, rather than creating a shower of colored flares, it breaks into just two pieces, a smaller piece of mass 1/5m and a larger piece of mass 4/5m. Both pieces land at exactly the same time. The smaller piece lands perilously close to the mortar (at a distance of zero from the mortar). The larger piece lands a distance d from the mortar. If there had been no explosion, the shell would have landed a distance r from the mortar. Assume that air resistance and the mass of the shell's explosive charge are negligible.
Find the distance d from the mortar at which the larger piece of the shell lands. Express d in terms of r.

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