The endless chasing scene between Tom and Jerry comes to a big, perfectly round lake. Jerry manages to escape Tom by a hair by plunging himself into the water. Tom can't swim - he can only run at a maximum speed of $v$ along the shoreline to try to catch Jerry. How fast must Jerry swim in order to land safely?
Started solving based on the (probably erroneous) assumption that Jerry would swim in a straight continuous line.
Jerry needs to swim the chord length 2*Rsin(a/2) where a is the angle that contains the chord
Tom needs to run the arc length aR
Toms time will be (a*R)/v this will also be Jerry's target time
So Jerry's speed needs to be 2
This chart shows the relationship between angle and necessary speed so Jerry's best bet is to swim across the lake when he has to swim faster then v*2/pi