Lecture-Ch3-Part-1-2024 PDF, Two Dimensional Kinematics

Chapter 3: Two Dimensional Kinematics Part 1 FIGURE 3.2 Motion in 1-dimension useful in some situations (e.g. drop ball) More realistic is 2-dimensional motion 3-dimensional motion realistic, but complicated. We will ignore VERTICAL & HORIZONTAL MOTIONS INDEPENDENT...

Chapter 3: Two Dimensional Kinematics Part 1 FIGURE 3.2 Motion in 1-dimension useful in some situations (e.g. drop ball) More realistic is 2-dimensional motion 3-dimensional motion realistic, but complicated. We will ignore VERTICAL & HORIZONTAL MOTIONS INDEPENDENT Two identical balls—one on left falls from rest, the one on the right has an initial horizontal velocity and is falling vertically. Arrows are velocity vectors. Horizontal (black) and vertical (green) velocity vectors at each position. Despite the difference in horizontal velocities, the vertical velocities and positions are identical for both balls. Shows that vertical and horizontal motions are independent. Independence of Perpendicular Motion https://www.youtube.com/watch?v=zMF4CD7i3hg https://www.youtube.com/watch?v=iO83zSqfGbc 1-D Addition of Vectors  Vector Addition – Head to Tail 1-d is simple: Total Displacement Example  1-D Addition of Velocity Vectors Person swimming (blue vector) Person swimming with current with no current (brown vector) Total velocity (pink arrow) https://www.youtube.com/watch?v=muqXSW1EZFs Person swimming against the current Total velocity (pink arrow)  Vector Addition – Head to Tail 2-d is simple: If the two vectors are at right angles (900) FIGURE 3.3 A pedestrian walks a two-dimensional path between two points in a city. In this scene, all blocks are square and are the same size. Total Distance Traveled = 14 blocks FIGURE 3.4 The Pythagorean theorem relates the length of the legs of a right triangle, labeled a and b , with the hypotenuse, labeled c. The relationship is given by: 𝑎 2 + 𝑏 2 = 𝑐 2. This can be rewritten, solving for 𝑐 = 𝑎 2 + 𝑏 2. FIGURE 3.5 The straight-line path followed by a helicopter between the two points is shorter than the 14 blocks walked by the pedestrian. All blocks are square and the same size. Total Distance Traveled = 10.3 blocks FIGURE 3.4 THE PYTHAGOREAN THEOREM The Pythagorean theorem relates the length of the legs of a right triangle, labeled a and b , with the hypotenuse, labeled c. The relationship is given by: 𝒂𝟐 + 𝒃𝟐 = 𝒄𝟐. 𝐎𝐑 𝒄= 𝒂𝟐 + 𝒃𝟐.  Trigonometric Functions 𝑩 sin(θ) = 𝑪 𝑨 cos(θ) = 𝑪 𝒔𝒊𝒏θ 𝑩 tan (θ) = = 𝒄𝒐𝒔(θ) 𝑨