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# Relative Motion Demo: The River Question

Ryan Thompson, OAPT Treasurer, Physics Teacher, Newmarket HS
superryanthompson@gmail.com

I purchased this little magnetic moon rover at Masterminds for \$6 a few years ago because I thought it was cool. I didn’t have any specific ideas on how to utilize it until a few years later when I was teaching the famous river question to students. You know how it goes: Alice is crossing a river that has a velocity with respect to the shore of 4 m/s [East] and Alice swims with a velocity of 3 m/s [South] with respect to the water. If the river is 60 m wide, how long does it take Alice to get to the other side? The concept that is hard for students to reconcile is that even though Alice is being pushed to the right from the shores frame of reference, the amount of time to get to the other side is independent of the river’s velocity. This is when I had a Eureka moment. I grabbed the moon rover and put it on our whiteboard. I then wound it up and let it go south, just like Alice would.

Images 1-2: This is from the river’s frame of reference.

As a class we agreed that it took a certain amount of time, t, to get to the other side of the river. Now, in my school, some of the whiteboards can actually slide to allow access to secret shelves, so I slid the board as if it was a river flowing while at the same time placing the moon rover at the start of the river crossing again. As I pushed the board, the moon rover went South and East from the students’ frame of reference but they had to agree that the time of the crossing was the same.

Images 3,4,5: This is from the Earth’s frame of reference.

I felt this was a powerful tool to help students conceptualize this very difficult idea. Now, I know what you are thinking: Ryan, what do I do if my whiteboard/chalkboard doesn’t slide? Well, you can cause the class to slide. Just have the students sidestep to the left as the rover goes down the board. Not only will you have the same effect but you can reinforce some more frames of reference ideas. Such as, who is doing the moving? Is it the river or the people on the shore? Does it matter in terms of the physics?