A cannon elevated at some angle ? (unknown) fires a shell with some initial spee

Question

A cannon elevated at some angle ? (unknown) fires a shell with some initial speed v (unknown) that has a range R when fired over level ground (see Figure (a)). 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, 26% of the shell (m2) continues onward and the other fragment (m1) falls straight down. Determine the distance D (in terms of R) that the forward moving fragment lands from the cannon .

Explanation / Answer

Center of mass travels the same path, unaffected.

So, m1*R/2 + m2*D = (m1+m2)*R

0.74m*R/2 + 0.26m*D = m*R

D = 2.423 R

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