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) How long, in seconds, does it take Phil to cross the river? Again, give the algebraic solution first and then a numerical answer. B )Assume the two boats left at the same exact moment and from the same spot. Write a single algebraic expression for the distance between two boats as a function of time (∆D(t) = ... ). Your expression may only use the variables VB, VW , θ and t.

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) How long, in seconds, does it take Phil to cross the river? Again, give the algebraic solution first and then a numerical answer. B )Assume the two boats left at the same exact moment and from the same spot. Write a single algebraic expression for the distance between two boats as a function of time (∆D(t) = ... ). Your expression may only use the variables VB, VW , θ and t.