Test on Vector Addition
Directions: Follow the Steps strictly.
Step 1: Sketch the given vectors.
Step 2: Make a chart/table to show the x and y components.
Template for chart
Vector
magnitude
Angle and direction
x-component
y-component
Summation of x and y components
Step 3: Plot the summation of X and the summation of Y
Step 4: Use PT to find the magnitude of the resultant vector and tan to find for the angle and direction.
Problem 1
A rural mail carrier leaves the post office and drives 22 km in a northerly direction. She then drives in
direction 60 degrees South of East for 47 km. Finally, she drives 30 km in a southerly direction. What is
the magnitude of her resultant vector?
Problem 2
Max plays middle linebacker for South's football team. During one play in last Friday night's game
against New Greer Academy, he made the following movements after the ball was snapped on third
down. First, he back-pedaled in the southern direction for 3.5 meters. He then shuffled to his left (west)
for a distance of 3 meters. Finally, he made a half-turn and ran downfield a distance of 5 meters in a
direction of 40° W of S before finally knocking the wind out of New Greer's wide receiver. Determine the
magnitude and direction of Max's overall displacement
Problem 3
A hiker's motion can be described by the following three displacement vectors. All angles are
measured from + x.
25.0 km, 45 degrees + 20.0 km, 140 degrees + 12.0 km, 285 degrees
Add the three displacement vectors using the head-to-tail method of vector addition. What is the
resulting displacement of the hiker?
Problem 4
During a rodeo, a clown runs 8 m north, turns 55 degrees N of E and runs 3.5 m. The, after waiting for
the bull to come near, the clown turns due 60 degrees W of S for 5 m and exit the area. What is the
clown’s total displacement?
Problem 5
During his first golf tournament (at age 2), Tiger Woods actually had to four-putt one of the holes
(meaning he had to putt the ball four times before it went in!). His putts were as follows: 10 meters
southwest, 3 meters north, 4 meters southeast, and 0.5 meters west. How far was the hole from his
original putting position? In what direction?
Problem 6: For 4B
f all the doggoned luck! The evil members of SAP have dognapped Dr. J's trusty three-legged dog,
Tripod, and are demanding a handsome ransom (one million autographed pictures of Dr. J plus $1.98).
The ransom note leads Dr. J on the following path:
From his house, he goes 100 km due east, turns, and then goes 500 km in a direction 30º north of east.
He then finds a bucket of Kentucky Fried Chicken that he quickly eats. (Trailing dognappers can make
you so hungry that you will woof down your food.) Upon licking his fingers, he finds his next directions
under his right thumbnail: Turn 45º south of east and go 100 km, then turn and go 350 km due north. At
this point, he finds evidence of Tripod-three paw prints and a stool. Further evidence that he is getting
close to his dog is the fact that the remaining instructions are written on the "bark" of a tree: Turn 40º
north of west and go 300 km, then turn 30º south of west and go 200 km. At long last, after dropping the
ransom in a container marked "SAP ransom-Drop Here," Dr. J. finds Tripod resting, propped against a
wall.
How far away and in what direction is Dr. J from home?