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Vector Addition Worksheet
Remember, the resultant vector must have both magnitude and direction.
Include a scale.
A = 35.00 km at 25o N of E
C = 20.0 km at 43o S of E
B = 15.0 km at 10.0o E of N
D = 40.0 km at 28o S of W
1. A + B
2. B + C
3. C + D
Solve all the following problems MATHEMATICALLY using your calculator.
Show all work. Remember, the resultant vector must have both magnitude and
direction (an angle).
4. Now, let’s assume that A, B, C, and D from above are each the resultant of 2
component vectors (x and y). Start by drawing each of these 4 vectors
separately and then determine what 2 vectors would be needed to produce
each one of them.
5. A boat is heading across a river at a velocity of 25 mph. The river is flowing
downstream at 10.0 mph. What is the actual velocity of the boat?
6. An airplane is flying 340 km/hr at 12o East of North. The wind is blowing 40
km/hr at 34o South of East. What is the plane’s actual velocity?
7. You are on an elevator that is plummeting toward the ground at 30.0 m/s and
you jump up right before it hits the ground. You jump upward with a velocity
of 5 m/s. At what speed do you hit the ground?
8. You push on a box with a force of 500.0 Newtons directly north. Another
person pushes the box with a force of 800.0 Newtons directly east. What is
the resultant force?
V. Find the angle measurements between the resultant vector and force vector
when two forces are applied to an object.
9. Two forces with magnitudes of 15 pounds and 10 pounds are applied to an
object. The magnitude of the resultant is 24 pounds. Find the measurement of
the angle between the resultant vector and the vector of the 10 pound force to
the nearest whole degree.
10. Two forces with magnitudes of 6 pounds and 18 pounds are applied to an
object. The magnitude of the resultant is 13 pounds. Find the measurement of
the angle between the resultant vector and the vector of the 18 pound force to
the nearest whole degree.
11. Two forces with magnitudes of 45 pounds and 62 pounds are applied to an
object. The magnitude of the resultant is 100 pounds. Find the measurement of
the angle between the resultant vector and the vector of the 45 pound force to
the nearest whole degree.
12. Two forces with magnitudes of 200 pounds and 340 pounds are applied to an
object. The magnitude of the resultant is 150 pounds. Find the measurement of
the angle between the resultant vector and the vector of the 200 pound force to
the nearest whole degree.
13. Two forces with magnitudes of 40 pounds and 42 pounds are applied to an
object. The magnitude of the resultant is 31pounds. Find the measurement of the
angle between the resultant vector and the vector of the 42 pound force to the
nearest whole degree. 13 lb 6 lb 18 lb 6 lb 18 lb 24 lb 20 lb 14 lb 14 lb 20 lb V.
Challenge Problems
14. Vector u has a magnitude of 53 and a direction of 0°. Vector v has a
magnitude of 10 and a direction of 295°. Find the magnitude and direction of the
resultant to the nearest whole number.
15. Vector u has a magnitude of 27 and a direction of 40°. Vector v has a
magnitude of 34 and a direction of 58°. Find the magnitude and direction of the
resultant to the nearest whole number.
16. Use vectors to answer the following questions.
a) If two forces from different directions are applied to an object, can the
magnitude of the resultant be larger than the sum of the magnitudes of the
forces? Justify your answer. b) What if the forces were from the same direction?
Justify your answer.