Unformatted text preview: Chapter 3
Motion in 2 Dimensions Resultant Vector sum of two or more vectors. The single vector that has the same overall effect of the vectors to be added. Vector addition in one dimension is easy, simply add or subtract the magnitude of the vectors Example: 4 m East + 3 m East = 7 m East (4+3) 4 m East + 3 m West = 1 m East (43) Vector addition in two (or more) dimensions isn't as easy: 4 m East + 3 m North is NOT 7 m Northeast Addition of Vectors Addition of Vectors: Graphical Method Rules for Graphical Addition of Vectors 1. Vectors may be moved as long as the magnitude (length) and direction do not change. 3. Vectors may be added in any order. 2. Vectors must be added tiptotail. 3. The resultant vector is draw from the tail of the first vector to the tip of the last. Vector Addition: Component Method Any vector can be resolved into components that lie along the xaxis and the yaxis. Called the x and y components and are found using the trig functions. Vector Addition: Component Method Example: Find the x and y components of the vector 500 m at 30 N of E. Vector Addition: Component Method Steps for Adding Vectors using Components 1. Draw a diagram and label each vector. 2. Choose x and y axes that will be most convenient. 3. Resolve each vector into its x and y components. Don't forget to pay attention to the sign of the components. 4. Create a component table to add all the x and y components together to obtain the resultant x and y components. 5. Combine the resultant vector components in to the resultant and calculate its magnitude and direction. Vector Addition: Component Method Example: Add these two displacement vectors: A: 40 km at 40 N of E B: 30 km at 35 W of N Example: Add these three velocity vectors. A: 18 m/s at 60 above the +xaxis B: 25 m/s in the negative xdirection C: 8 m/s at 10 below the +xaxis Projectile Motion Projectile motion is motion in two dimensions (or components) at the same time: horizontal and vertical. Must treat each component separately. Each component will have its own displacement velocity, and acceleration, but will share the same time. All projectiles follow a parabolic path (ignoring air resistance). Projectile Motion: Problem Solving
1. Sketch a diagram. 2. Set an xy plane and choose which directions will be positive and negative. 3. List the known and unknown variables. (Be sure to resolve the velocity in to its components if necessary) 4. Approach each component separately with time as the common factor to solve for the unknown values. Projectile Motion: Examples A rescue plane drops a package from a height of 100 m while traveling at 40 m/s. A. How far from the point the package is dropped does it land? B. What is its velocity upon impact? Projectile Motion: Examples A long jumper leaves the ground at an angle of 20.0 above the horizontal at a speed of 11.0 m/s. A. How far does he go? B. What is his maximum height? Projectile Motion: Examples A human cannonball will be launched with a velocity of 25 m/s at an angle of 35 above the horizontal into a large net that will be suspended 5 meters above the level of the cannon. How far away must this net be placed? ...
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