Dr. L. and his cat Kepler are coming home from fishing. They ended their trip on the south bank of a 1200 m wide river, directly across from where Caroline is waiting to pick them up on the north bank. They are in identical boats that travel at 4 m/s (VB) on still water. The river is normally ‘lazy’ and flows with negligible velocity. On a calm day, if they pointed the boats north, they would cross the river in exactly 300s. However, today, the river is flowing due east with a constant velocity (VW) of 1 m/s relative to the ground. Kepler, because she doesn’t know better (she is a cat after all), has not taken this into account. Without paying attention, Kepler keeps the boat pointed due north for the entire trip. A) Relative to the ground, what is Kepler’s velocity? Derive an algebraic solution (in terms of VB and VW only) and then give a numerical answer (three significant figures is fine) expressed in degrees relative to due north (e.g. ‘42.3° west of north’).
Dr. L. and his cat Kepler are coming home from fishing. They ended their trip on the south
bank of a 1200 m wide river, directly across from where Caroline is waiting to pick them up
on the north bank. They are in identical boats that travel at 4 m/s (VB) on still water. The
river is normally ‘lazy’ and flows with negligible velocity. On a calm day, if they pointed the
boats north, they would cross the river in exactly 300s. However, today, the river is flowing
due east with a constant velocity (VW) of 1 m/s relative to the ground. Kepler, because she
doesn’t know better (she is a cat after all), has not taken this into account. Without paying
attention, Kepler keeps the boat pointed due north for the entire trip.
A) Relative to the ground, what is Kepler’s velocity? Derive an algebraic solution
(in terms of VB and VW only) and then give a numerical answer (three significant figures is
fine) expressed in degrees relative to due north (e.g. ‘42.3° west of north’).
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