Question

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.

Answer 1

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

Let O denote an observer. Then

`v_(A/B)=v_(A/O)+v_(O/B)=v_(A/O)-v_(B/O)`

where
`v_(X/Y)` denotes the velocity of a body X relative to another body Y. We're told that

`v_(A/O)=10(\rm m)/(\rm s)`

and

`v_(B/O)=-15(\rm m)/(\rm s)`

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

`v_(A/B)=(10-(-15))(\rm m)/(\rm s)=25(\rm m)/(\rm s)`