A boat that can travel 15 km/hr in still water wants to cross a river 1 km wide

Question

A boat that can travel 15 km/hr in still water wants to cross a river 1 km wide by traveling from east to west. The river is flowing 5 km/hr to the south. (a) if the boat driver wishes to land the boat at a dock on the other side of the river directly opposite his starting point, answer the following: in which direction should the boat drive point the boat?; find the vector expression for the boats velocity relative to the earth; how long does it take him to cross the river. (b) instead, if the boat driver points his boat directly at the dock opposite his starting point, answer the following: where is the boat when ti reaches the opposite shore?; find the vector expression for the boats velocity relative to the earth.

Explanation / Answer

(a) the direction he should drive his boat is

arcsin(5/15) = 19.47 degrees south of west

the boat's velocity relative to the EARTH would be

speed = 15cos19.47 = 14.14

velocity: 14.14 km/hr WEST

time = 1km / 14.14 km/hr = 0.0707 hours = 4.24 minutes

(b) where is the boat? it is

1 * 5 / 15 = 0.333 km north of the dock

vector expression for velocity: 15 km/hr WEST + 5 km/hr NORTH

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