The boat in the figure is heading due north as it crosses a wide river with a ve

Question

The boat in the figure is heading due north as it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due east. Determine the velocity of the boat with respect to an observer on the riverbank.

http://www.webassign.net/sercp9/3-figure-24.gif

Suppose the river is flowing east at 3 m/s and the boat is traveling south at 4 m/s with respect to the river. Find the speed and direction of the boat relative to Earth.
speed ______ m/s
direction ________

Explanation / Answer

The boat's velocity has two components: North 10 and East 5. Start by determining the scalar speed, using the Pythagorean theorem: s² = 10² + 5² s² = 125 s = 11.18 km/hr To determine the velocity, we need to know the direction as well as the speed. For that, we find the angle whose tangent is 5 / 10. f = arctan(5 /10) f = arctan(.5) f = 26.6° So the boat's v is 11.18 km/hr at 26.6° east of north.

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