Vector (Relative velocity question)

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SUMMARY

The discussion centers on a relative velocity problem involving two ships, A and B. Ship A travels north at 7 km/h, while Ship B appears to move southeast at 12√2 km/h. The calculated direction of Ship B is E22.6°S, but the provided answer is N67°23'E. The discrepancy arises from a misunderstanding of the reference direction for Ship B's velocity vector, which should be clarified for accurate interpretation.

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  • Understanding of vector addition and unit vectors
  • Familiarity with trigonometric functions, specifically tangent
  • Knowledge of navigation directions (e.g., North, South, East, West)
  • Basic principles of relative velocity in physics
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  • Study vector addition in physics, focusing on relative velocity scenarios
  • Learn about unit vectors and their applications in navigation
  • Explore trigonometric functions, particularly how to use them for angle calculations
  • Review common navigation conventions and how to interpret directional angles
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Students studying physics, particularly in mechanics and vector analysis, as well as educators looking to clarify concepts of relative motion and navigation.

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Homework Statement



An observer, on a ship A sailing to the north with speed of 7km/h, saw a ship B. Ship B seems to be moving to south-east with a speed of 12√2 km/h.

Find the direction which B is heading to.

Homework Equations


The Attempt at a Solution



Let i and j be the unit vectors in the direction of eat north respectively and VA = velocity of ship A and VB = velocity of ship B.

Now, VA = 7j

BVA = 12i - 12j

VB
= BVA + VA
=12i - 5j

so θ = tan-15/12 = 22.6°

The direction of ship B is E22.6°S.

But the answer given is N67°23'E, which step is incorrect? Can anyone enlighten me?
 
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Michael_Light said:
The direction of ship B is E22.6°S.

But the answer given is N67°23'E, which step is incorrect? Can anyone enlighten me?
Your answer looks fine to me. Are you sure the book's answer wasn't S67°23'E, which would be pretty close to yours.
 

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