Physics 12 - Quiz #6

Boats on a River

Solution:

 
a) The vector equation for the velocity of the boat with respect to the water is given by,
 

VAW = VAS + VSW

  where VAS =  5.0 m/s with the course 300 North of East

            VWS = 1.5 m/s in the direction of South

thus,

           VSW = 1.5 m/s in the direction of North

 

We can now draw the vector diagram the represents the vector equation. 

 

 

We can now solve for VAW.


   

 b) The distance upstream is easily solved by determining the time of crossing using VASx and

then calculating vertical displacement using VASy.

 
c) The vector equation for the velocity of the boat with respect to the shore is given by,
 

VBS = VBW + VWS

  where VBW =  2.5 m/s with a heading of 550 South of East

            VWS = 1.5 m/s in the direction of South

 

The vector diagram should be drawn to aid in seeing the following calculations.

 

d) The time to cross the river is then simply calculated using the width of the river and the

x-component of VBS.

 
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