1. Relative Motion
All Motion is Relative

2. Motion in the Same Line
When motion is in the same line (whether positive or negative), the velocities are added.
VA/B = VA + VB
This is used for opposite directions
(ie. – North and South)

3. Motion at Right Angles
When motion is at right angles, the Pythagorean Theorem can be used.
VA/B2 = VA2 + VB2
This requires that the directions be at 90 degrees.
ie. – North and East

4. Motion at non-right Angles
When motion is not at right angles, the vertical and horizontal components must be found for one of the velocities.
These components are combined with the other to get velocities at right angles.
VA = V sin θ
VB = V cos θ

5. Question 1
1) A hiker walks 4.5 km north in one direction, then makes a 45° turn to the right and walks another 7.4 km. What is the magnitude of her displacement?

6. Question 2
2) What is the magnitude of your displacement when you follow directions that tell you to walk 310 m south then make a 50° turn to the left and walk 120 m?

7. Question 3
3) A car moving east at 50 km/hr passes a truck traveling northeast at 25 km/hr. What is the magnitude of the velocity of the truck relative to the car?

8. Question 4
4) A motorboat heads due northeast at 15 m/s relative to the water across a river that flows due north at 6.0 m/s. What is the velocity of the motorboat with respect to the shore?

9. Question 5
5) An airplane flies due southwest at 155 m/s with respect to the air. There is a wind blowing at 60 m/s to the north relative to the ground. What is the plane’s speed and direction with respect to the ground?

10. Question 6
6) You are driving up a long inclined road. After 750 m you notice that signs along the roadside indicate that your elevation has increased by 200 m. What is the angle of the road above the horizontal?

11. Question 7
7) A lighthouse that rises 55 m above the surface of the water. A sailor on the deck of a ship sights the top of the lighthouse at an angle of 12.0° above the horizontal. If the sailor’s eye is level to the water, how far away is the ship?