Vector Addition:
I know you can't physically do drawings on this site. Is there a way of someone explaining how to begin with this problem. Can I chose any scale.
The directions said to use the head to tail method to determine the resultant vector of the following velocity vectors.
V1= 40m/s @35 degrees
V2= 55m/s @260 degrees
V3= 75m/s @133 degrees
V4= 20m/s @190 degrees
https://www.youtube.com/watch?v=OrryaQqcvk8
Sure! I can explain how to approach the problem of vector addition using the head to tail method without the need for physical drawings.
1. First, let's start by understanding the head to tail method. This method involves placing the tail of one vector at the head of the previous vector to create a connected chain of vectors.
2. Begin by selecting a scale that is convenient for you. The scale helps establish the relative lengths of the vectors in your diagram. You can choose any scale you prefer, as long as it remains consistent throughout the problem. For example, you could choose 1 cm to represent 10 m/s.
3. Start by drawing the first vector, V1, according to its magnitude and direction. To do this, draw an arrow representing the direction and length of V1. Since V1 is given as 40 m/s at 35 degrees, draw an arrow that is 4 cm long at an angle of 35 degrees from the reference line (usually the positive x-axis).
4. Next, take the tail of the first vector and place it at the head of the second vector, V2. V2 is given as 55 m/s at 260 degrees. Draw an arrow representing V2, starting from the head of V1. Make sure the length of the arrow represents the magnitude of V2 according to the chosen scale, which in this case would be 5.5 cm long. The angle should be measured from the reference line.
5. Proceed to connect the tail of V2 to the head of V3. V3 is given as 75 m/s at 133 degrees. Draw an arrow representing the direction and magnitude of V3, starting from the head of V2 and following the scale we chose. In this case, the arrow should be 7.5 cm long at an angle of 133 degrees.
6. Finally, connect the tail of V3 to the head of V4. V4 is given as 20 m/s at 190 degrees. Draw an arrow representing the direction and magnitude of V4, starting from the head of V3 and using the chosen scale. The arrow should be 2 cm long at an angle of 190 degrees.
7. The resulting vector, which connects the tail of V1 to the head of V4, represents the resultant vector obtained by adding all the individual vectors together. Its magnitude and direction can be determined by measuring the length and angle of this final vector.
Remember, you can adjust the scale to fit your drawing sheet or use a different unit of measurement as long as you remain consistent throughout the diagram.