However, what made today's class interesting was coming face-to-face with a most formidable topic; it is known to physicists and experienced firsthand by swimmers and pilots.
Prepare to have your mind blown as I attempt to explain the inner workings of:
Relative Velocities
Origin: Kinematics - Motion in Two Dimensions
Definition:
- Wikipedia: In non-relativistic kinematics, relative velocity is the vector difference between the velocities of two objects, as evaluated in terms of a single coordinate system.
- TL;DR: Relative velocity is looking at how fast something is moving from different *points of view. *Note: Points of view are referred to as frames of reference.
Difficulty: Medium
We are all aware of relative velocities and may not even know of it.
Try to remember a windy day where you were walking outside.
When trying to walk in a straight line, a gust of wind (say, 60 km/h) would push you to the left/right and it would force you to readjust your path so that you don't walk into the road.
Someone watching you from above in a helicopter may see the following triangle form.
Adding a little more meaning to this triangle yields this:
The questions in the textbook basically had us use trigonometric formulas and functions to solve for missing angles/sides.
To find the hypotenuse, we would use the Pythagorean Theorem:
a² + b² = c²
5² + 8² = c²
25 + 64 = c²
89 = c²
89 = c²
c ~9.4 km/h
Next, we need to to find the angle formed at the starting position
TanΘ = opposite/hypotenuse
TanΘ = 8/5
TanΘ = 8/5
Θ ~ 58°
The resulting vector is therefore 58° East of North at 9.4 km/h.
Other questions may require using Sine Law or Cosine Law to find missing sides, but this is all basically trigonometry.
The practice questions we did in class were on page 118, #59 and #60.
