AP* PHYSICS B DESCRIBING MOTION: KINEMATICS IN TWO DIMENSIONS &VECTORS

To discuss objects that move in something other than a straight lines. Vectors have both magnitude AND direction while scalars have only magnitude. Velocity, displacement, force and momentum are vectors. Speed, mass, time and temperature are scalar quantities. Vectors--arrows drawn to show direction and the length of the arrow is % to magnitude straight line we need vectors.

A small heavy box of emergency supplies is dropped from a moving helicopter at point A as it flies along in a horizontal direction. Which path in the drawing at the right best describes the path of the box (neglecting air resistance) as seen by a person standing on the ground?

2-Dimensional Motion Definition: motion that occurs with both x and y components. Example: Playing pool. Throwing a ball to another person. Each dimension of the motion can obey different equations of motion.

ADDITION OF VECTORS Graphical, tedious method--tip to tail. If the motion or force is along a straight line, simply add the two or more lengths to get the resultant. More often, the motion or force is not simply linear. That’s where trig. comes in. You can use the tip to tail graphical method, BUT you’ll need a ruler and a protractor.

Solving 2-D Problems Resolve all vectors into components x-component Y-component Work the problem as two one-dimensional problems. Each dimension can obey different equations of motion. Re-combine the results for the two components at the end of the problem.

Adding Vectors

ADDITION & SUBTRACTION OF VECTORS Graphical, tedious method--tip to tail. If the motion or force is along a straight line, simply add the two or more lengths to get the resultant. More often, the motion or force is not simply linear. That’s where trig. comes in. You can use the tip to tail graphical method, BUT you’ll need a ruler and a protractor.

Introduction We have learned how to add and subtract vectors that are parallel or anti-parallel. In so doing we have taken two or more vectors and found their resultant (displacement), which is a vector that can take the place of the other vectors.

Trigonometry

Trigonometry Functions

Start by drawing a set of axes at the “head” of the vector (its origin if you prefer). The x and y-components lie along their respective axes (b) and their magnitudes are equal to:

To get the direction (angle): Use trig. functions—

What we will need? We will need to be given the direction of the two components which we will be asked to find. In this situation, we will find the horizontal and the vertical components (velocity, acceleration, or displacement for this chapter.)

A ball’s velocity can be resolved into horizontal and vertical components. 5.3 Components of Vectors

Resolving the velocity Then proceed to work problems just like you did with the zero launch angle problems.  VoVo V o,y = V o sin  V o,x = V o cos 

What we will need We will need to be given a vector. The vector we will use as an example will be in this case velocity.

NOW THE PYTHAGOROUS TO FIND TOTAL VELOCITY V 2 = V x 2 + V y 2