Use principles of component addition of vectors with the Pythagorean theorem and SOH CAH TOA to solve the following vector addition problems.
Mia Ander exits the front door of her home and walks along the path shown in the diagram at the right (not to scale). The walk consists of four legs with the following magnitudes:
A = 80.0 meters
B = 281.0 meters
C = 127.0 meters
D = 180.4 meters
Determine the magnitude of Mia's resultant displacement.
Resultant's Magnitude
meters
Determine the direction of Mia's resultant.
Resultant's direction
° CCW from East
Spring break has just begun and Latonya boards a plane to visit her Grandma. Latonya flies 705.6 miles due East from City A to City B. After a short layover, Latonya flies 544.1 miles in a direction of 38.8° north of east from City B to City C.
What is the magnitude of Latonya's resultant displacement between city A and city C?
Resultant's magnitude
miles
What is the direction of Latonya's resultant displacement?
Javar is at the dog park with Roscoe, his Labrador Retriever. Roscoe catches a scent of interest and walks 29.9 meters south, then 25.8 meters at an angle 31.0 degree north of east, and finally 49.7 meters west.
Find the magnitude of Roscoe's resultant displacement.
m
Find the direction of Roscoe's resultant displacement.
Dora is exploring a cave. She starts at the entrance and makes the following straight-line movements:
64.9 meters, south
108.7 meters, 25.1° North of West
35.3 meters, south
187.4 meters, 16.2° South of East
Determine Dora's position relative to the entrance of the cave. How far is Dora from the cave entrance?
In what direction is Dora from the cave entrance?
°CCW from East