1. Sep 7, 2010

### jollyrancher9

A ferry cross a river of width d. The speed of the boat is v relative to the water, and the speed of the tidal current is w parallel to the riverbanks. The ferry landing points are directly opposite each other on each side of the river. How long does the shortest return trip take?

My attempt: vector v and vector w add to form vector v+w, which is directionally a straight line between the 2 ferry landing points. Then, (v+w) = d/t, and t = d/(v+w), where d, v and w are all vectors. Is this correct? The answer seems too simplistic.

Thanks to everyone for taking the time to look at this. Your help is much appreciated!

Best,
jollyrancher99

2. Sep 8, 2010

### housemartin

Hello!
v and w are not parallel. Ferry crosses river - its velocity is perpendicular to the riverbank and river flows parallel to the riverbanks. So you can't write t = d/(v+w). For ferry to travel perpendicularly to the riverbank, component of v along riverbank must cancel velocity of the tidal current w. Guess this helps.