1. Vector addition

2. Andreas walked 5 meters east away from a tree
Andreas walked 5 meters east away from a tree. Then, he walked 3 meters north. Finally, he walked 1 meter west. I’m not sure where he was going, but find Andreas’s total displacement from the tree.
Explain what your answer means.

3. A train is moving to the west at 20 m/s, the attendant on the train is moving towards the rear of the train at 5 m/s serving drinks. While walking to the rear of the train a Mountain Dew bottle that nobody wants falls on its side and rolls towards the back of the serving cart. The bottle rolls at 2 m/s. Sketch the problem and determine the velocity of the bottle as seen by a person outside the train.
Explain what your answer means.

4. A riverboat heads east on a river that flows north
A riverboat heads east on a river that flows north. The riverboat is moving at 5.1 m/s with respect to the water. The water moves north with respect to the shore at a speed of 3.6 m/s.
a. Sketch!
b. Determine the resultant velocity of the riverboat (velocity with respect to the shore…how would it look to an observer?).
c. If the river is 71.0 m wide, then determine the time required for the boat to cross the river.
d. Determine the distance the boat will travel downstream.
e. What happens to time if the velocity of the water is increased?

5. 1. Velocity of boat (w.r.t. water) = 3.2 m/s, East
1. Velocity of boat (w.r.t. water) = 3.2 m/s, East
Velocity of river (w.r.t. shore) = 4.4 m/s, South
Width of river = 127 m
a. Resultant velocity:
magnitude =
direction =
b. Time to cross river =
c. Distance downstream =
2. Velocity of boat (w.r.t. water) = 2.6 m/s, West
Velocity of river (w.r.t. shore) = 4.2 m/s, South
Width of river = 96 m

6. A plane heads 45o at a speed of 200 m/s
A plane heads 45o at a speed of 200 m/s. the wind is blowing at a heading of 270o with a speed of 60 m/s. Determine the resulting velocity of the plane as compared to a person on the ground.
**use VAD and table method**
Explain what your answer means.

7. ** use VAD and table method**

8. Three students are discussing the resultant magnitude of two added vectors. Vector A has a magnitude of 5 centimeters, and vector B has a magnitude of 3 centimeters.
Alexis: “We’d have to know the directions of the vectors to know how big the resultant is going to be.”
Bert: “Since we are only asked about the magnitude, we don’t have to worry about the directions. The magnitude is just the size, so to find the magnitude of the resultant we just have to add the sizes of the vectors. The magnitude of the resultant in this case is 8 centimeters.”
Cara: “No, these are vectors, and to find the magnitude you have to use the Pythagorean theorem. In this case the magnitude is the square root of 34, a little less than 6 centimeters.”
Dacia: “The resultant is the vector that you have to add to the first vector to get the second vector. In this case the resultant is 2.”
Which, if any, of these students do you agree with?
Alexis _____ Bert _____ Cara _____ Dacia_____ None of them______
Explain.

9. Alexis is correct!
Direction matters!!

10. Shown below are vector diagrams representing two sets of forces.
1. List all the forces that have a zero x-component 2. List all the forces that have a zero y-component 3. List all the forces that have an x- component pointing in the positive x- direction 4. List all the forces that have a y- component pointing in the negative y-direction

11. Answer:
1. G
2. CE
3. DBFE
4. BFH

13. None of them!
Solution 1 and 2 are both possible solutions…on solution 3, the components are not perpendicular!

15. Answer:
ABF=EGHCD

17. Answer:
Both are direction B

19. Determine the missing values:
Compass heading
East reference
Cardinal
140o
240o
30o S of E

20. A plane heads 45o N of W at a speed of 200 m/s
A plane heads 45o N of W at a speed of 200 m/s. the wind is blowing at a heading of 30o S of E with a wind speed of 60 m/s. Determine the resulting velocity of the plane as compared to a person on the ground.
**sketch and table method**
Explain what your answer means.