Relative Velocity Problem: Boat Chasing and Stone Throwing

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SUMMARY

The discussion centers on calculating the relative velocities of two boats and a stone thrown from one boat. Boat A, moving at 40 miles per hour relative to the river, is chasing Boat B, which travels at 48 miles per hour relative to the river. The stone is thrown horizontally from Boat B at 23 miles per hour relative to the boat. The key calculations involve determining the horizontal velocity of the stone relative to both Boat A and the riverbank, with the positive direction defined as the direction of the boats' motion.

PREREQUISITES
  • Understanding of relative velocity concepts
  • Basic knowledge of vector addition
  • Familiarity with motion in a river current
  • Ability to perform calculations involving speed and direction
NEXT STEPS
  • Study the principles of relative velocity in physics
  • Learn about vector addition and subtraction in motion problems
  • Explore examples of motion in a current, such as boats in rivers
  • Investigate the effects of horizontal and vertical velocity components
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Students of physics, educators teaching motion concepts, and anyone interested in solving relative velocity problems in real-world scenarios.

mike1
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A boat A is chasing boat B along a river by moving in the same direction as the
stream. The speed of the river stream is 6 miles per hour, the speed of boat B relative to
the river is 48 miles per hour, and boat A is 8 miles per hour slower than boat B.
Currently boat B is ahead of boat A, and a person throws a stone horizontally at boat A at a
speed 23 miles per hour relative to their boat.

What is the horizontal velocity of the stone relative
to boat A and to the river bank? [What are the positive direction of motion and indicate what the origin is]


I let the direction of boat A and B be the positive direction.
Boat A have a relative velocity of Xp=40 and boat B have a relative velocity of Xq=48.
Relative velocity of boat B to boat A Xqp=48-40=8
Am I right in letting the relative velocity of the brick Xb= -23, because its going backwards and now how do I calculate Xbp? or is that the wrong approach?
 
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