The video above illustrates the independence of horizontal versus vertical motion. Motion is relative and different reference frame will measured different velocities.
Read carefully the textbook for section 4.3. The ideas are simple but it can become quite confusing when solving problems.
Section 4.3 is a great place to do careful reading as we discussed in week 1B "Reading and Studying Methods". The method is as follows.
To avoid mistakes when solving relative motion problem it is really important to use the proper notation.
Here is an example. In the following we have a car denoted C (or toy truck really) moving on a sheet of plastic (denoted S) which is itself moving with respect to the ground (G).
There are three different velocities and the relationship between them is
Typical problems in relative motion are crossing a river and distinguishing between the velocity relative to water and velocity relative to ground. These are very similar problems to the airplane problem example 4.7 and 4.8.
Try to do both examples 4.7 and 4.8 on your own before looking at Knight's solution.
Q. Rain is falling with a speed of 2 m/s with respect to the ground at angle of 30° from the vertical (counterclockwise from the -y axis; see picture). A car drives through the rain at a constant velocity, such that the rain appears to the driver of the car to be falling straight down along the vertical. What is the velocity of the car with respect to the ground?
The worksheet for this problem is available here