What Direction and Distance Must the Ship Sail to Reach 125km East of Guam?

AI Thread Summary
To determine the direction and distance a ship must sail to reach 125 km east of Guam after initially sailing 300 km at an angle of 32 degrees north of west, the resultant displacement calculations are essential. The ship's initial position is broken down into components, resulting in a displacement vector that needs to be adjusted to achieve the target position. The calculations show that the ship must head at an angle of approximately 50.9 degrees south of east and travel a distance of about 204.99 km. It's crucial to maintain a consistent reference system throughout the calculations to avoid confusion. Properly interpreting the problem statement clarified the intended destination as east rather than west.
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Homework Statement


A ship leaves the island of Guam and sails a distance 300km at an angle 32.0∘ north of west.

In which direction must it now head so that its resultant displacement will be 125km directly east of Guam? (Express your answer as an angle measured south of east)

How far must it sail so that its resultant displacement will be 125km directly east of Guam?

Homework Equations

The Attempt at a Solution


A [/B]= 300km @ 32 deg
B = 125 km @ 180 deg

Ax = 300cos(180-32) = -254.41 Ay = 300sin32 =158.98
Bx= -125 By = 0
A-B = C
Cx = -129.41 C y= 158.98

C= sqrt(-129.41^2 + 158.98^2)
C = 204.99

0(theta) = arctan (y/x) = arctan (158.98/ 129.41) = -50.9 south of east
 
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Your choice of direction references in this problem is confusing and non-standard.

A vector heading of due east from the origin is given an angle of 0 degrees, and the angles increase in a counterclockwise direction, so that due north is 90 deg., due west is 180 deg., and due south is 270 deg.

The Attempt at a Solution


A [/B]= 300km @ 32 deg
B = 125 km @ 180 deg
The angles given above are non-standard and confusing.
Ax = 300cos(180-32) = -254.41 Ay = 300sin32 =158.98
In the calculation of the components above, you seem to use the standard direction references.

Bx= -125 By = 0
A-B = C
Cx = -129.41 C y= 158.98

Now, it appears you are using a different reference system.

C= sqrt(-129.41^2 + 158.98^2)
C = 204.99

0(theta) = arctan (y/x) = arctan (158.98/ 129.41) = -50.9 south of east

In order to prevent from becoming hopelessly confused, first make a sketch of the problem. Use one set of coordinate directions and stick to it throughout the calculation.
 
Thank you for your reply steamking. I reread the question after your suggestion and realized my mistake was thinking they wanted to end up 125k west of guam. Thanks again.
 

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