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A 9.0 kg shell is fired at 50 m/s at 55° above level ground…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A shell is fired at at above level ground. At the top of its path it bursts into two pieces: a piece that falls straight down, and a piece. Ignoring air and taking , where does each piece land?
Need a reminder? The key ideaShow
Only external forces move the centre of mass: . With no external force, the total momentum is conserved, and the centre of mass stays at rest or moves steadily.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. The centre of mass keeps to the shell's parabola.
Step 1. Range. .
Step 2. The light piece. It falls from the top, at .
Step 3. The heavy piece. , so .
Answer: and from the gun.
Check. Both land at the same time (both fall from the same height with no vertical speed), so the centre of mass rule applies at landing.
Watch out. If the pieces did not land together, the rule would hold only until the first one hit the ground.
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