AP Physics 1 Name: ____________________________________________________________________________ Period: __ Date: ____
Vectors Worksheet
[Addition and Resolution Notes and problem set] (Note: Homework must go on separate sheet and retained)
What is a Vector?
Vectors are graphic representations of physical occurrences. We use vectors to visualize what physically happens to an object under certain
conditions. Vectors designate the magnitude and direction of things like forces, accelerations, velocities, and displacements. They help us to
describe motion through a common symbology.
Magnitude - the amount of the force, acceleration, velocity, or displacement.
Direction - a specific direction in which the force is applied, or the
Acceleration, velocity, or displacement occur.
What is Vector Addition?
Vector addition is the process of finding the resultant vector when given the components of the vector.
In one-dimensional vector addition, you will be working on either the x (horizontal) or y (vertical) axis. The vector addition is simply the addition
(or subtraction if the vectors are in opposite directions) of the two vectors. If they are in opposite directions, the resultant direction will be in the
same direction as the vector with the greatest magnitude.
In two-dimensional vector addition, you have both an x (horizontal) and a y (vertical) component. You add the vectors by using the Pythagorean
Theorem since the two vectors are at right angles to each other. This value is the magnitude of the result vector. The direction of the result
vector is the angle between the hypotenuse of the triangle and the horizontal. To find this value, you use the tan -1 function on the calculator.
What is Vector Resolution?
Vector resolution is used in two-dimensional vector analysis and is the reverse to vector addition. In vector resolution, you know the magnitude
and direction (angle) of the resultant vector and you are solving for the horizontal and vertical components.
To find the x (horizontal) component, you use the cosine function and the formula: Rx = Rcosθ; where R is the magnitude of the resultant
To find the y (vertical) component, you use the sine function and the formula: Ry = Rsinθ; where R is the magnitude of the resultant
Finding Resultant magnitude and direction
1.
A truck driver attempting to deliver some furniture travels 8 km east, turns around and travels 3
km west, and then travels 12 km east to his destination.
a. What distance has the driver traveled?
b. What is the driver’s displacement?
2. While following the directions on a treasure map, a pirate walks 45.0 m north, then turns and
walks 7.5 m east. What single straight-line displacement could the pirate have taken to reach
the treasure?
3. Homework: Emily passes a soccer ball 6.0 m directly across the field to Kara, who then kicks the
ball 14.5 m directly down the field to Luisa. What is the ball’s total displacement as it travels
between Emily and Luisa?
Resolving Vectors
1. How fast must a truck travel to stay beneath an airplane that is moving 105 km/h at an angle of
25° to the ground?
2. What is the magnitude of the vertical component of the velocity of the plane in item 1?
3. A truck drives up a hill with a 15° incline. If the truck has a constant speed of 22 m/s, what are
the horizontal and vertical components of the trucks velocity?
4. What are the horizontal and vertical components of a cat’s displacement when it has climbed 5
m directly up a tree?
5. Find the horizontal and vertical components of the 125 m displacement of a superhero who files
down from the top of a tall building at an angle of 25° below the horizontal.
6. Homework: A child rides a toboggan down a hill that descends at an angle of 30.5 to the
horizontal. If the hill is 23.0 m long, what are the horizontal and vertical components of the
child’s displacement?
7. Homework: A skier squats low and races down an 18° ski slope. During a 5 second interval, the
skier accelerates at 2.5 m/s2. What are the horizontal (perpendicular to the direction of free-fall
acceleration) and vertical component of the skier’s acceleration during this time interval?