This question makes ZERO sense to me at all
“While Louise is running at 6.0m/s to the right, a ball rolls at 4.0m/s to the left. Calculate the speed of the ball relative to Louise”
I’ve tried to find a simulation to help you understand this concept. Try this one.
When you give the red cyclist a velocity, lets say 3m/s to the right. The stationary observer would see this as a velocity of 3 m/s to the right. However from the perspective of the green cyclist, moving a 10 m/s to the left (or -10 m/s), the red cyclist would seem to be getting closer by 13 metres every second. This hopefully makes sense if you think about oncoming traffic seeming faster when you’re driving towards it (hopefully on the other side of the road). Whereas a car moving towards you while you are standing still doesn’t seem as fast.
For example, when you’re standing still, a car travelling at 13.8 m/s (50kph) towards you would seem to be travelling at 13.8 m/s.
However if you were moving towards it at 11.1 m/s (40kph) at the same time as it was driving towards you at 13.8 m/s (50kph), from either drivers perspetive the other vehicle would seem to be getting closer at a rate of 24.9 m/s (90kph). So for objects approaching one another, their relative speed is simply the sum of their individual speeds. Once the vehicles pass each other, each would see the other as receeding at 24.9 m/s.
This becomes a little more tricky if we want to understand relative velocity, as one velocity might be negative but the other positive. I’ll expand on that if you ask me to. It rarely comes up in exams, in fact I don’t believe it is covered under the L2 mechanics standard, so you shouldn’t need to stress over it for your exam.
Coming back to your problem: from Louise’s perspective, how rapidly would the ball seem to be getting closer to her?
What would be the speed of the ball relative to Louise if the ball and Louise were moving to the left?
would the speed of the ball relative to Louise be 10m/s?
Awesome, yes - well done!
If you want to test your understanding:
If they were both moving to the left at those speeds (6.0m/s for Louise and 4.0m/s for the ball), what would the speed of the ball be relative to Louise then?
I think it might be -2m/s?
Yes, the relative speed of the ball is 2m/s relative to Louise.
The negative sign is tricky, as it indicates direction. The negative sign would suggest the ball is behind Louise, and getting further from her at 2m/s.
However, if Louise is to the right of the ball (both still travelling to the left), then the ball would be getting closer to Louise at the rate of 2m/s. Since we don’t know where they started in relation to each other - we can’t say for sure if the relative velocity is 2m/s or -2m/s. However the relative speed is 2m/s either way.
By including the negative sign, we are beginning to talk about relative velocity. Just like relative speed, but now with the added complexity of direction.
I hope you feel a bit more confident about that concept. Don’t worry about it for your exam though.
thank you, that actually helped a lot
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