This series of caches is reaching the end of its run.
I will be archiving them in August 2022
It is recommended, but not necessary, that you complete the puzzles in order as each puzzle will have an increasing level of difficulty. The puzzles in the series are
Physics Puzzle #1 (GC6XBGC)
Physics Puzzle #2 (GC6XDN0)
Physics Puzzle #3 (GC6XDXM)
Physics Puzzle #4 (GC6XK5Q)
Physics Puzzle #5 (GC6XMW4)
Physics Puzzle #6 (GC6XP3J)
Physics Puzzle #7 (GC6XXY3)
Physics Puzzle #8 (GC6XY1H)
Physics Puzzle #9 (GC6XY50)
The Lesson
As before, you will be looking at vectors which are measured quantities that require a direction. The two parts of a vector are magnitude and direction.
For this puzzle, you have to think back to your high school days when you learned about the Pythagorean Theorem and the use of "tan" from Trigonometry.
Pythagoean Theorem: a2 + b2 = c2
Trigonometry tanθ = opposite/adjacent
(The Greek letter θ is used as a general symbol to represent an angle)
Both of these are used with right triangles. Note: None of my diagrams are to scale! I am also rounding off to the nearest degree, kilometre, or metre
A common type of problem, that uses vectors, occurs in navigation. When an airplane is flying, airspeed and ground speed are two of the quantities that are considered. Airspeed is the speed of the plane relative to the air. Think of airspeed as how fast the plane would go if the air was still (no wind). Ground speed is the speed of the plane relative to the ground. This would be how fast the plane appears to go when viewed from the ground. If the air is still, ground speed and airspeed are the same. What happens when the air is moving? The effect of these two quantities adds together as vectors. But, it is not as simple as adding the magnitudes. Directions must also be considered.
Example: A small airplane has a cruising speed of 190 km/h and maintains a heading due south. What will be the ground speed if there is a crosswind blowing at 50 km/h to the west.
When the direction was introduced, the speeds became vectors. When vectors are added together they are placed "tip-to-tail" meaning you draw the vectors so that the tail of one is placed at the head of the one before. The sum of vectors is called the resultant and it drawn from the tail of the first vector to the head of the last. It doesn't change the resultant if you change the order of the vectors - so there is no correct order. The direction for the resultant vector (or any vector) is always measured at the tail of the vector.
For the example...
The resultant velocity for this example is 196 km/h [195°].
The Puzzle
Your task is to find the resultant velocity for the following problem.
The same small plane is flying at 190 km/h [east] while there is a wind blowing at 65 km/h [south]. Find the plane's ground speed.
Enter the digits of your answer in the spaces provided
___ ___ ___ [ ___ ___ ___°]
A B C [ D E F°]
For your final problem...
A pilot, in our plane, wants to maintain a heading due north while the wind is blowing to the east at 60 km/h. What heading should he fly in order to have the desired velocity? Round off any calculations to two decimal places until you get to the final answer.
[___ ___ ___°]
[ G H J°]
A = __ B = __ C = __ D = __ E = __ F = __ G = __ H = __ J = __
The cache can be found at N 44° ab.cde’ and W 078° fg.hjk’
There is no connection between the upper case letters above and the lower case letters here.
a = G - D: _____; b = F - G - J: _____; c = G J: _____;
d = J G: _____; e = A + G + J: _____; f = (C + D) J: _____;
g = H E: _____; h = J ÷ C: _____.
j = F + (B)(D): _____; k = A G + D: _____.
The cache is at: N 44° __ __ . __ __ __ ' and W 078° __ __ . __ __ __'
You can check your answers for this puzzle on GeoChecker.com.