Use Pythagorean theorem, SOH CAH TOA, and a head-to-tail vector addition diagram to solve the following right-angle vector addition problems.
It’s Dante's first day of school at South and he is learning to navigate the hallways. Dante is in the East wing and walks a distance of 27.2 meters eastward followed by another eastward walk of 42.1 meters.
What is the magnitude of Dante's resultant displacement?
Resultant magnitude
meters
What is the magnitude of Dante's resultant displacement in a situation in which the 42.1 m walk is in the westward direction, opposite the 27.2 m walk? (Enter a + value.)
Jim Nazium is walking from lunch to his PE class. He exits the lunchroom and walks 41.0 meters west. He then turns and walks 67.8 meters north down the hallway leading to the locker room.
Determine the magnitude of Jim's resultant displacement.
m
Determine the direction of Jim's resultant displacement. Express as a counterclockwise angle of rotation from East.
Resultant direction
° CCW from East
Ken Fused is in a corn maze and makes three consecutive displacements which put him back at his starting point. The first two displacements are 24.8 meters, west and 47.8 meters, north.
Find the magnitude of the third displacement.
3rd Vector magnitude
Find the direction of the third displacement. (Use the counterclockwise from east convention.)
3rd Vector direction
degrees from 0˚ east
A student was doing a physics lab and made the following displacements through the hallways. Each leg of the trip was carefully measured. The results of the measurements are as follows:
A = 2.0 meters
B = 12.3 meters
C = 18.2 meters
D = 33.7 meters
E = 4.2 meters
Determine the resulting displacement's magnitude of the physics student.
Resultant's magnitude
Determine the resulting displacement's direction of the physics student.
Resultant's direction
During the Vector Addition lab, Mac and Tosh start at the classroom door and walk …
43.5 meters, north,
31.7 meters east,
16.3 meters south,
60.1 meters west, and
4.4 meters, north.
Determine the magnitude of the resultant displacement of Mac and Tosh.
Determine the direction of the resultant displacement of Mac and Tosh. Express your answer as a counter-clockwise angle of rotation from East.
Sheila is captain of the Varsity cross country team. During the after-school practice on Tuesday, she led the team on the following run from school to a nearby park where they met the coach for a meeting:
0.64 miles, north;
1.02 miles east;
1.52 miles north;
0.26 miles, west.
Determine the magnitude of the team's resultant displacement.
Determine the direction of the team's resultant displacement. Express your answer as a counter-clockwise angle of rotation from East.