Boat A & B's Motion: Initial Position & Velocity

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SUMMARY

The discussion focuses on the motion of two boats, A and B, defined by their parametric equations. Boat A's position is described by x=3-t and y=2t-4, while Boat B's position is given by x=4-3t and y=3-2t. The initial positions of both boats can be determined by substituting t=0 into their equations. To find the velocity vectors, differentiation of the position equations is required. Additionally, the angle between the paths and the time at which the boats are closest to each other are key points of analysis.

PREREQUISITES
  • Understanding of parametric equations in motion
  • Knowledge of differentiation techniques
  • Familiarity with vector representation of velocity
  • Basic trigonometry for angle calculations
NEXT STEPS
  • Study the differentiation of parametric equations
  • Learn how to calculate velocity vectors from position functions
  • Research methods for finding the angle between two vectors
  • Explore techniques for determining the minimum distance between moving objects
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Students in physics or mathematics, educators teaching motion concepts, and anyone interested in understanding parametric equations and their applications in real-world scenarios.

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Boat A's position is given by the parametric equation x=3-t, y= 2t -4 where position is km and time is hours. Boat B's poisiton is given by x=4-3t, y= 3-2t

a) find the initail position of each boat
b) find the velocity vector of each both
c) what is the angle between the paths of the boat
d) at what time are the boats closest to each other

I have NO CLUE on how to start the question
 
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No clue? That's bad news. For a) try putting t=0. The bad news is that it gets more complicated after that. For b) and d) you have to differentiate. Can you at least try?
 

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