A mouse moves indefinitely along a straight line with speed u. A cat starts off the mouse's line and always runs directly towards it with constant speed v. Which condition guarantees eventual capture?
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A mouse moves indefinitely along a straight line with speed u. A cat starts off the mouse's line and always runs directly towards it with constant speed v. Which condition guarantees eventual capture?

G1 Physics · Accepted Answer

For pure pursuit on an unbounded plane, the pursuer must have greater speed than the target for guaranteed finite-time capture from a generic off-line initial position.