A mouse runs along +x with constant speed u. A cat starts at perpendicular distance a from the mouse's initial line and runs with constant speed v>u, always directly towards the mouse. The capture time is:
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Question

A mouse runs along +x with constant speed u. A cat starts at perpendicular distance a from the mouse's initial line and runs with constant speed v>u, always directly towards the mouse. The capture time is:

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G1 Physics · Accepted Answer

For pure pursuit with initial line of sight perpendicular to prey velocity, integration of the pursuit equations gives t_c=av/(v²−u²). It is not the simple one-dimensional closing-time expression.