Vector Addition and Resolution Practice Problems
Vector Addition and Resolution Practice Problems
1. Calculate the resultant velocity of Freda Flyer who normally flies at 100 km/h and then encounters a 10 km/h headwind (a wind coming from ahead).
2. Calculate Freda Flyer’s speed in a 10 km/h tailwind (coming from behind).
3. Calculate the resultant velocity of a pair of 100 km/h velocities at right angles to each other.
4. A certain right triangle has sides of 3, 4, and 5. If two vectors of magnitude 3 and 4 are at right angles to each other, what is their resultant?
5. If a 5 unit vector has a vertical component of 3 units, what is its horizontal component?
6. If a 5 unit vector has a vertical component of 4 units, what is its horizontal component?
7. If a 14 unit vector makes an angle of 45o with the horizontal, what are its horizontal and vertical components?
8. An experimental jet plane, just after takeoff, climbs with a speed of 500 km/h at an angle of 37o with the horizontal. At what rate is the plane gaining altitude?
9. If the sun is directly above the jet plane in the preceding problem, how fast does the shadow of the plane travel across the ground?
10. A plane can travel with a speed of 80 mi/hr with respect to the air. Determine the resultant velocity of the plane (magnitude only) if it encounters a
a. 10 mi/hr headwind.
b. 10 mi/hr tailwind.
c. 10 mi/hr crosswind.
d. 60 mi/hr crosswind.
11. A motor boat traveling 5 m/s, East encounters a current traveling 2.5 m/s, North.
a. What is the resultant velocity of the motor boat?
b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?
c. What distance downstream does the boat reach the opposite shore?
12. A motor boat traveling 5 m/s, East encounters a current traveling 2.5 m/s, South.
a. What is the resultant velocity of the motor boat?
b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?
c. What distance downstream does the boat reach the opposite shore?
13. A motor boat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South.
a. What is the resultant velocity of the motor boat?
b. If the width of the river is 120 meters wide, then how much time does it take the boat to travel shore to shore?
c. What distance downstream does the boat reach the opposite shore?
14. If the current velocity in question #13 were increased to 5 m/s, then
a. how much time would be required to cross the same 120-m wide river?
b. what distance downstream would the boat travel during this time?
15. Barb Dwyer recently submitted her vector addition homework assignment. As seen below, Barb added two vectors and drew the resultant. However, Barb Dwyer failed to label the resultant on the diagram. For each case, which is the resultant (A, B, or C)? Explain.
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16. Consider the following five force vectors.
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Sketch the following and draw the resultant (R). Do not draw a scaled vector diagram; merely make a sketch. Label each vector. Clearly label the resultant (R).
A + C + D
B + E + D
17. On two different occasions during a GBS soccer game, the ball was kicked simultaneously by players on opposing teams. In which case (Case 1 or Case 2) does the ball undergo the greatest acceleration? Explain your answer.
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18. Billie Budten and Mia Neezhirt are having an intense argument at the lunch table. They are adding two force vectors together to determine the resultant force. The magnitude of the two forces are 3 N and 4 N. Billie is arguing that the sum of the two forces is 7 N; Mia argues that the two forces add together to equal 5 N. Who is right? Explain.
19. Matt Erznott entered the classroom for his physics class. He quickly became amazed by the remains of some of Mr. Schott's whiteboard scribblings. Evidently, Mr. Schott had taught his class on that day that:
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Explain why the equalities are indeed equalities and the inequality must definitely be an inequality.
20. The following picture is hanging in the White House. For each picture, use trigonometric functions to determine the weight of the picture.
[pic]
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