[Many thanks to Ralph Tadday for developing this material]
We will talk about Rock Climbing in this Lab. During Rock climbing, you secure yourself and your friends from falling, by securing a rope to you and to the rock by fixing a rope to hooks you put or find in the rock. You can imagine that not every hook is perfectly above you when you fall, so again, we do need to understand vectors. This is a review about how to add and subtract vectors. If it all is easy – great! The document is a bit long, because I added some review meant to help you in case you need to refresh your memory.
Now these components Ax and Ay we just defined help us adding vectors. As long as you know how long the arrow A is, and you know in which direction it points you can imaging, that there is some way to calculate the length of the shadow of this arrow, when you put a lamp to the left (this shadow is called Ay, and when you have a lamp on top (this shadow is called Ax). The sin and cos are the mathematical tools that help you to calculate the length of Ax and Ay. Can you see that Ay would be the same length as the arrow A when the arrow A is perpendicular? Can you see how long Ax is for a perpendicular arrow A? We can add Ax and Ay just like numbers, or just like we added vectors in the 1 dimensional world we lived in during the first two weeks of class.
