Adding Non-Perpendicular Vectors Worksheet
KEY
Name:________________
____________
Date:_________________
Mod:_________________
Directions: Solve the problems below by using the component method of vector addition to find the resultant. Make sure that
the resultant has both magnitude and direction because it is a vector quantity. Show all work by setting up the chart and
showing the equations for each problem and circle your final answer. Make sure to include correct units.
1.
Solve for the resultant displacement of the two vectors:
A = 2.3 km @ 45 degrees
B = 4.8 km @ 90 degrees
A
B
R
x
1.63 km
0.00 km
1.63 km
y
1.63 km
4.80 km
6.43 km
∆𝑦
𝜃 = tan−1 ( )
∆𝑥
𝑅 = √∆𝑥 2 + ∆𝑦 2
𝑅 = √1.63𝑘𝑚2 + 6.43𝑘𝑚2
6.43𝑘𝑚
𝜃 = tan−1 (
)
1.63𝑘𝑚
𝑅 = 6.63 𝑘𝑚
𝜃 = 75.78°
𝑅 = 6.63 𝑘𝑚 @ 75.78°
2.
A hiker walks due east for a distance of 25.5 km from her base camp. On the second day, she walks 41.0 km North
West till she discovers the cave she wanted to see. Determine the magnitude and direction of her resultant
displacement between the base camp and the cave.
3. x
y
A 25.50 km
0.00 km
B -28.99 km 28.99 km
R -3.49 km 28.99 km
−∆𝑥
𝑅 = √∆𝑥 2 + ∆𝑦 2
𝜃 = tan−1 (
) + 90°
∆𝑦
𝑅 = √−3.49𝑘𝑚2 + 28.99𝑘𝑚2
−(−3.49𝑘𝑚)
𝜃 = tan−1 (
) + 90°
28.99𝑘𝑚
𝑅 = 29.20 𝑘𝑚
𝜃 = 96.86°
𝑅 = 29.20 𝑘𝑚 @ 96.86°
3.
An airplane heads north of east by 18 degrees for a distance of 67 km then heads due north for 39 km. What is the
planes total displacement?
A
B
R
x
63.72 km
0.00 km
63.72 km
y
20.70 km
39.00 km
59.70 km
∆𝑦
𝜃 = tan−1 ( )
∆𝑥
𝑅 = √∆𝑥 2 + ∆𝑦 2
𝑅 = √63.72𝑘𝑚2 + 59.70𝑘𝑚2
59.70𝑘𝑚
𝜃 = tan−1 (
)
63.72𝑘𝑚
𝑅 = 87.32 𝑘𝑚
𝜃 = 43.13°
𝑅 = 87.32 𝑘𝑚 @ 43.13°
Adding Non-Perpendicular Vectors Worksheet
Methacton High School Physics Department
1
4.
Solve for the resultant velocity of the vectors below:
A = 3.7 m/s @ 0 degrees
B = 1.5 m/s @ 38 degrees
C = 6.1 m/s @ 90 degrees
D = 2.2 m/s @ 160 degrees
A
B
C
D
R
x
3.70 m/s
1.18 m/s
0.00 m/s
-2.07 m/s
2.81 m/s
y
0.00 m/s
0.92 m/s
6.10 m/s
0.75 m/s
7.77 m/s
∆𝑦
𝜃 = tan−1 ( )
∆𝑥
𝑅 = √∆𝑥 2 + ∆𝑦 2
𝑚2
𝑚2
7.77𝑚
𝑠
𝜃 = tan−1 (
)
2.81𝑚
𝑠
𝑅 = √2.81 𝑠 + 7.77 𝑠
𝑅 = 8.26
𝑚
𝑠
𝜃 = 70.11°
𝑚
𝑅 = 8.26 𝑠 @ 70.11°
5.
A red fox leaves his den and heads out to find mice. The fox travels due west for a distance of 2.1 km. He then picks
up the scent of field mice and then cuts south west for a distance 0.8 km where is finds a nest full of mice. What is
the fox’s total displacement from his den to the nest full of mice?
A
B
R
6. x
-2.10 km
-0.57km
-2.67 km
y
0.00 km
-0.57 km
-0.57 km
∆𝑦
𝜃 = tan−1 ( ) + 180°
∆𝑥
𝑅 = √∆𝑥 2 + ∆𝑦 2
𝑅 = √−2.67𝑘𝑚2 + −0.57𝑘𝑚2
−0.57𝑘𝑚
𝜃 = tan−1 (
) + 180°
−2.67𝑘𝑚
𝑅 = 2.73 𝑘𝑚
𝜃 = 192.05°
𝑅 = 2.73 𝑘𝑚 @ 192.05°
Adding Non-Perpendicular Vectors Worksheet
Methacton High School Physics Department
2