We will practice going between reference frames
to look at relative velocities in one dimension.
Let's say that an observer is standing on the sidewalk
and that observer sees a car drive
past to the right at a speed of v car.
The observer also sees a bike that's
riding to the left at a slower speed, v bike.
Now, I'm interested in what the car looks
like from the perspective of the bike.
The bike sees itself as stationary
and sees the world around it moving to the right.
To the bike, the observer on the sidewalk
appears to be moving to the right with the speed of v bike.
The car was moving to the right relative to the reference
frame of the observer standing on the sidewalk.
So to the bike, the car looks like it's
going even faster to the right with a total speed
of v car plus v bike.
Let's say, later on the biker throws an apple
in the direction of her movement and sees this apple travel
to the left with the speed of v apple.
Now I want to know what an observer sees
in the stationary frame on the sidewalk.
The apple appears to be traveling a speed v
apple faster than the biker all to the left.
So the observer on the sidewalk will see the apple move
to the left with a total speed of v apple plus v bike.
Now let's say the person throws the apple forward
at a speed v apple.
What does the car see?
To the car the apple is going to the left at the speed of v
car minus v apple.
How about the bike?
To the bike, the apple is going at a speed of v apple plus v
bike to the right.