Relative Velocity: Solving Boat Race Circuits

AI Thread Summary
The discussion revolves around a relative velocity problem involving a power boat racing around three buoys in an equilateral triangle, with a current affecting its path. The boat's cruising speed is 60 km/hr, and it must navigate from buoy A to buoy B, which is 5 km east, while accounting for a 10 km/hr current from the southwest. The calculations for the first leg of the race (A to B) indicate that the boat should be steered at an angle of approximately 6.77 degrees to counteract the current, taking about 270 seconds to complete this leg. However, further calculations for the leg from B to C cannot proceed without additional information about buoy C's exact location. The conversation highlights the importance of precise data for solving relative velocity problems in navigation.
CloudKel
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Homework Statement



Relative velocity question. A power boat has cruising speed of 60 km/hr. It is
taking part in a race around three buoys arranged in an equilateral triangle. The
second buoy, B, is 5 km due East of the starting/finishing buoy, A. The third
buoy, C, is to the North of the line joining A and B. There is a current flowing at
10 km/hr from the south-west. In what direction should the boat be steered on
each leg of the race and how long will it take the boat to complete one circuit.


Homework Equations



Vb = Vb/w + Vw



The Attempt at a Solution


A to B
Vw = 5(square root 2)i + 5(square root 2)j
Vb/w 60Cos(theta)i + 60Sin(theta)j
Vb = 5(square root 2) + 60Cos(theta)i + 5(square root 2)+ 60Sin(theta)j

5(square root 2)+ 60Sin(theta)j = o
Sin(theta) =5(square root 2) / 60
theta = 6.77

5(square root 2) + 60Cos(6.77)i =66.65i
Vb = 66.65i + 0j
t = 0.075hrs
t = 270.068s
 
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Welcome to PF, CloudKel!
Those answers for AB are correct. I don't see how you can do the rest unless you get more specific information about the location of C.
 
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