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Graphical Methods of Vector Addition

Practice Graphical Methods of Vector Addition
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Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

A boat that is starting at point A is attempting to sail across a river to get to point B. If the current in the river is flowing in the downward direction, what direction should the boat point itself before setting sail?

Why It Matters

  • If the current in the image shown is directed downward, when the boat sets sail towards point B, the current would cause the boat to miss its mark. This is because as the boat sails in the horizontal direction, it will begin to pick up a vertical velocity that is oriented in the downward direction. Therefore, the further the boat has to travel along the horizontal axis to get to the other side, the further away downward from point B it would be.
  • To take into account that velocity imparted on the boat by the flowing river, the captain of the boat would need to orient the boat in a direction so that the boat travels into the flowing river. To figure out what direction the captain should point his boat, he would simply calculate the angle from the ratio of the velocity of the river and the velocity of the boat relative to the water:

\sin \theta = \frac{V_{river}}{V_{boat - river}}

  • By doing this, the captain takes into account the amount the boat would drift by the time the other side is reached and would orient his boat towards point C.

Credit: Bob Heims, U.S. Army Corps of Engineers
Source: http://en.wikipedia.org/wiki/File:Drift_boat_aka_Mckenzie_River_dory.jpg
License: CC BY-NC 3.0

The rough currents make it difficult to direct the boat [Figure2]


Can You Apply It?

Using the information provided above, answer the following questions.

  1. If the velocity of the river relative to the ground is 5 mph and the velocity of the boat relative to the ground is 10 mph, at what angle would the boat need to set sail from point A to make it to point B?
  2. At what point would the equation given above become invalid?

Image Attributions

  1. [1]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0
  2. [2]^ Credit: Bob Heims, U.S. Army Corps of Engineers; Source: http://en.wikipedia.org/wiki/File:Drift_boat_aka_Mckenzie_River_dory.jpg; License: CC BY-NC 3.0

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