1. Vectors and Scalars
AP Physics C

2. Applications of Vectors
VECTOR ADDITION – If 2 similar vectors point in the SAME direction, add them.
Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started?
ANSWER: 84.5 m +
Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION.
84.5 m

3. Applications of Vectors
VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT.
Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started?
ANSWER: 24.5 m EAST -
24.5 m east \

4. Adding Vectors Algebraically
In order to add vectors algebraically, you must do the following:
Resolve each vector into components (For vector A, find Ax and Ay. For vector B, find Bx and By. And so on)
Add like components to find components of the resultant. (Rx=Ax +Bx +…, Ry=Ay+By+…)
Find magnitude of resultant and direction of resultant (|R|= √(Rx2 + Ry2 )

5. Example 1 12 m, W ANSWER:R =26.93 m, Ө=31.3 degrees Or R=23i + 14j
A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.
12 m, W
ANSWER:R =26.93 m, Ө=31.3 degrees Or
R=23i + 14j
6 m, S
20 m, N
35 m, E
R= m, θ= i + 14j

6. Example 2
A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.
Answer: R =17 m/s, Ө=28.1 degrees west of north OR R=-8i + 15j
8.0 m/s, W
15 m/s, N Rv q
R = 17 m/s, θ=28.1 degrees west or noth i + 15 j

7. Example 3
A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components.
HC=53.85i VC= j
H.C. =? 32
V.C. = ?
63.5 m/s
53.85 I – 33.64j

8. Example 4 Find the sum of two vectors A and B lying in the xy plane.
Find A - B
A = 2.00i j
B =5.00i -4.00j
ANSWER:
A-B = -3i + j

9. Example 5
A particle undergoes three consecutive displacements: Δr1 = (1.50i j -1.20k)cm,Δr2=(2.30i – 1.40j -3.60k)cm, and
Δr3=(-1.30i j)cm. Find the components of the resultant displacement and its magnitude.
ANSWER:
R= 2.5i+3.1j -4.8 k
|R|=√(2.5)2 +(3.1)2 +(1.5)2
|R|=6.24 cm
2.5i +3.1j-4.8k cm

10. Example 6
A hiker beings a two day trip by walking 25.0 km due southeast from her car. She stops a sets up her ten for the night. On the second day she walks 40.0 km in a direction 60 degrees north of east, at which point she discovers a ranger’s tower.
Determine the components of the hikers displacement in each day.
Determine the components of the hiker’s total displacement for the trip.
a) 17.7i -17.7j and 20.0i j b)37.7i +16.9j
a) 17.7i-17.7j b) 37.7i j