Vector Components Vectors 2

Vector Components It is possible to regard a single vector as the resultant (R) of two component vectors: one acting horizontally (x) and the other vertically (y). Vector resolution is the process of determining these two components.   x (horizontal) y (vertical) R

Using Vector Components The purpose of vector components is to find the result when coplanar vectors are added Coplanar vectors are those that exist in the coordinate plane (not necessarily at right angles)

Adding Vectors Using Components Step 1: Determine the x and y components of each vector using sine and cosine. Step 2: Add all the components in the x direction keeping in mind direction of each x component. Add all the components in the y direction (keep in mind direction) Step 3: Use the Pythagorean theorem on the added values to find the resultant vector. (final answer) Step 4: To find the angle of the resultant vector, use

Example: In a soccer game, Player A kicks a ball 15.0m at an angle of 30.0⁰ N of E. Player B intercepts it and kicks it 18.0m 20.0⁰ S of E to score on goal. What is the ball’s resultant displacement? Step 1: Calculate the x and y components of each vector. Draw a diagram for A. Calculate the components. Don’t forget the compass rosette. 15.0m Ay 30.0⁰ Ax

Draw a diagram for B. Calculate the components. Bx 20.0⁰ By 18.0 m

Step 2: Add the x components Step 2: Add the x components. Remember in this case that both vectors have east x components (that means they are both positive.) Add the y components. One is north and the other is south so one will be negative when they are added.

Step 3: use the sums of the components to find the magnitude of the resultant vector using the Pythagorean Theorem. (A resolved diagram must be drawn at this stage.) Step 4: Use the sums of the x and y components to calculate the angle of the resultant using tan. Write the answer in a sentence.