Name_______________
Vectors: Graphical and Algebraic
1.) Michael drives his BMW 30 km at a heading 20o North of East (v1). He then turns to a heading
15o West of South (255 o) and travels for 45 km (v2).
a. Draw this situation to scale, on graph paper. (Make sure you draw a scale.)
b. Draw the RESULTANT vector. Measure it’s magnitude and direction and report here.
Vr = ___________________
c. Break the vector up into components (graphically). Write each component below.
V1x = ___________________
V1y = ___________________
V2x = ___________________
V2y = ___________________
d. Add up these components to give resultant components.
Vx = ___________________
Vy = ___________________
e. Combine the vectors from d. into a single vector. Be sure to report both MAGNITUDE
and DIRECTION.
Vr = ____________________
f.
Now do the entire problem algebraically. What is the resultant vector? (Show work
below.)
Vr = ____________________
2.) Philip pogo-sticks for 55 m at a heading 15o above the –x axis (165 o) (v1). He then turns to a
heading 30o left of the +y axis (120 o) and travels for 20 m (v2).
a. Draw this situation to scale, on graph paper. (Make sure you draw a scale.)
b. Draw the RESULTANT vector. Measure it’s magnitude and direction and report here.
Vr = ___________________
c. Break the vector up into components (graphically). Write each component below.
V1x = ___________________
V1y = ___________________
V2x = ___________________
V2y = ___________________
d. Add up these components to give resultant components.
Vx = ___________________
Vy = ___________________
e. Combine the vectors from d. into a single vector. Be sure to report both MAGNITUDE
and DIRECTION
Vr = ____________________
f.
Now do the entire problem algebraically. What is the resultant vector? (Show work
below.)
Vr = ____________________
Conclusion
1. Compare and contrast solving problems like these graphically versus algebraically.
2. What are the strengths and weaknesses of the graphical method?
3. What are the strengths and weaknesses of the algebraic method?
4. Describe a situation in which the graphical method would be the best to use. (Be specific!)
5. Describe a situation in which the algebraic method would be the best to use. (Be specific!)
6. What conclusions can you draw about the graphical versus the algebraic method to solve vector
problems?