Relative Velocity: Solving Boat Race Circuits

[CloudKel]

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

 

[Delphi51]

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.