Beetle harvest

Classical Mechanics Level 3

A scout from an ant colony (colony A) finds a dead beetle of mass \(M\) a distance \(d_A\) from his colony. At the same time, a scout from another colony (colony B) who is distance \(d_B\) from his colony, also finds the beetle. If ants from colony B can walk at speed \(v_B\), and workers from \(A\) can each carry the mass \(\delta m\) of ant flesh at any given time, what is the slowest speed (in m/s) at which workers from colony A walk so that workers from colony B never catch up and steal the beetle pieces?

Details

If an ant from colony B catches an ant from colony A, it will kill the ant from colony A.
If an ant from colony A makes it to colony A with beetle flesh, he is safe from workers from colony B.
The scouts both start out at the beetle.
\(d_A=3\) m
\(d_B=5\) m
\(v_B=5\) m/s
\(M=250\) g
\(\delta m=0.5\) g

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.