castillorenee17
castillorenee17 castillorenee17
  • 10-10-2019
  • Mathematics
contestada

If Car A is moving 10 m/s east and Car B is moving 15 m/s west.

What is the speed of Car A relative to B.

Include answer and direction without unit.

Respuesta :

LammettHash
LammettHash LammettHash
  • 10-10-2019

Car A is moving at a speed of 25 m/s east relative to Car B.

Let O denote an observer. Then

[tex]v_{A/B}=v_{A/O}+v_{O/B}=v_{A/O}-v_{B/O}[/tex]

where [tex]v_{X/Y}[/tex] denotes the velocity of a body X relative to another body Y. We're told that

[tex]v_{A/O}=10\dfrac{\rm m}{\rm s}[/tex]

and

[tex]v_{B/O}=-15\dfrac{\rm m}{\rm s}[/tex]

where we take east to be to the positive direction. Then

[tex]v_{A/B}=(10-(-15))\dfrac{\rm m}{\rm s}=25\dfrac{\rm m}{\rm s}[/tex]

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