**Motion in Two Dimensions:** Crosswinds and Projectile Motion

**Motion in Two Dimensions:**

__Reading__

BJU book: Ch. 5 "Motion in a Plane"

__Topics__

Now we're working in 2 dimensions

We will spread this topic over two sessions:

- Crosswinds or 'cross river' type problems
- Projectile motion problems

Below: The "airplane-wind" example illustrates the classic "crosswinds" problem. The 'apparent speed' of the plane and the 'wind speed' are resolved into a 'resultant' ground-speed vector.

Below: In "projectile motion" problems, we separate the 'x' and 'y' components and solve them separately using the 5 equations of motion.

__Lecture outline:__

Be able to use the 5 equations of motion to solve problems in 2 dimensions.

Be able to use "SOH-CAH-TOA" to solve problems

- Sine = opposite/hypotenuse
- Cosine = adjacent/hypotenuse
- Tangent = opposite/adjacent

Be able to solve these classic two-dimensional Physics problems:

- Flying an airplane in a crosswind
- Canoeing across a flowing river
- Projectile Motion problems, such as firing a cannon or kicking a socker ball

To solve these problems and determine the resultant vector 'R', follow this sequence:

- Draw a nice, big sketch
- Resolve the individual vectors (typically 2 or 3) into their 'x' and 'y' components
- Then, to solve for the 'x' and 'y' components of the resultant vector, add the 'x' and 'y' components of the individual vectors together. BE CAREFUL OF SIGNAGE HERE.
- Determine the angle of the resultant vector 'R' using SOH-CAH-TOA
- Determine the magnitude of the resultant vector 'R' using the Pythagorean theorem.

When solving Projectile Motion problems:

Know the difference between Scalars and Vectors

- Treat the horizontal and vertical components separately
- Assume there is no horizontal acceleration once the projectile leaves the gun, or after the soccer ball is kicked (as the case may be)
- Other than that, there is nothing really 'unique' about solving projectile motion problems

Know the difference between Scalars and Vectors

- A scalar quantity has "magnitude" only. Examples: 1) an airplane flies at 50 m/s... 2) a man walks at 1.5 m/s.
- A vector has magnitude AND direction. Examples: 1) an airplane flies due north at 50 m/s... 2) a naval gun fires at a horizontal angle of 20 degrees and a muzzle velocity of 800 m/s.

__Surveying Lab (continued)__

Outdoor surveying lab: Vectors

We will use commercial surveying equipment (transit-level) to determine the distance of a far-away object (more than 1 mile away) using nothing but angles and vector measurements.

Then we will compare our calculated distance with Google Earth to see how close we came.

If we do this carefully, you may be surprised at how close we come to the 'actual' distance.

__Lab Extension assignment__

3._surveying_for_a_new_bridge__vectors_lab_extension_.pdf |

__Homework (refer to class emails for due dates)__

3._projectile_motion_simulation.docx |

3._2-d_motion_problems.docx |