Vectors and Projectiles Legacy Problem #2 Guided Solution

As is often the case, this is not a very mathematically oriented problem, it just simply requires arithmetic addition and subtraction. But the difficulty of the problem is understanding that it doesn't require exactly that addition and subtraction. So what you have to do is picture Rosa in her boat, and she is paddling upstream in Part A. Relative to the water, she's moving 1.2 meters per second. That is, if you could ignore everything else, you would know that Rosa moves 1.25 meters per second along the water. But you can't ignore everything else, because this question is about how fast she's moving relative to the banks. You see, the river isn't stationary, but the river flows down the river. And she's paddling up the river against the current. And so if you want to find out how fast she's going relative to the banks, consider a second. In one second, she is traveling up the water 1.25 meters, but then the water is traveling back the opposite direction, down the river, 0.5 meters in that one second. And so what you do is you take the upward velocity, upstream velocity, 1.25, and you subtract the 0.5 from it. And what you get is 0.75 meters per second upstream. And then in Part B, you do something very similar. You consider Rosa paddling downstream in the direction of the current. And in this situation, she's traveling 1.25 meters relative to the water, but the water moves along as well, 0.5 meters per second relative to the banks. So now with these two vectors in the same direction, you add them up to get 1.75 meters per second downstream.