Use principles of component addition of vectors with the Pythagorean theorem and SOH CAH TOA to solve the following vector addition problems.
Dora is exploring a cave. She starts at the entrance and makes the following straight-line movements:
62.7 meters, south
107.1 meters, 21.8° North of West
32.9 meters, south
186.4 meters, 15.5° South of East
Determine Dora's position relative to the entrance of the cave. How far is Dora from the cave entrance?
Resultant's magnitude
meters
In what direction is Dora from the cave entrance?
Resultant's direction
°CCW from East
Taylor and Drew finish their last class on the day before Spring break and decide to take a spontaneous road trip. Their trip involves the following movements:
45.0 miles, 69.6° North of West
54.4 miles, West
20.8 miles, 19.9° West of South
Taylor's car breaks down after the last leg of the trip.
How far are Taylor and Drew from campus?
miles
In what direction are Taylor and Drew from campus?
° CCW from East
Sasha begins her morning run. Her jog begins from her garage with a displacement of 24.0 meters west to the street. Sasha turns on to the street and continues to the first stoplight. When at the stoplight, Sasha is 42.3 meters away from her garage at an angle of 23.5 degrees North of West.
What was the length of her second displacement?
2nd vector's length
m
What was the direction of the second displacement?
2nd vector's direction
Mr. H is trying to manage an ant invasion in his home. He watches as an ant walks 12.4 cm, South across his kitchen floor. The ant then walks 15.6 cm at 35.1° East of South.
What is the magnitude of the ant's displacement?
cm
What is the direction of the ant's displacement?
Consider two displacements vectors – A and B – having the same length of 3.3 meters. Vector A has a CCW direction (counter-clockwise from east) of 156.9° and Vector B has a CCW direction of 256.6°.
Find the magnitude of A + B using component analysis.
Find the direction of A + B using component analysis.