1. Aim: How do we add vectors graphically to solve for relative velocities?

2. Do Now:
An ant is crawling on the sidewalk. At one moment, it is moving south a distance of 5.0 mm. It then turns 45 degrees south of west and crawls 4.0 mm. What is the magnitude of the ant’s displacement?

3. Relative Velocity
The relative velocity is a measure of how fast the velocity of an object as measured by an observer.

4. Tailwind
How fast is the plane moving relative to an observer on the ground? 125 km/h

5. Headwind
How fast is the plane moving relative to an observer on the ground? 75 km/h

6. Crosswind
The plane is flying south. The wind is blowing west. How fast is the plane moving relative to an observer on ground? 103 km/h

7. Visualizing Relative Velocities

8. Relative Velocity Problems
When we add displacement vectors, we find the resultant displacement. When we add velocity vectors, the resultant can represent the relative velocity.

9. Visualizing Relative Velocity

10. Riverboat Velocity Problem 1 (Solve Graphically)
A boat is traveling across a river that flows due east at 8.50 m/s. The compassheading of the boat is 30.0° north of east. Relative to the water, the boat is traveling straightforward (in the direction in which the boat is pointing) at 11.2 m/s. How fast and which way is the boat moving relative to the banks of the river?

12. Riverboat Velocity Problem 2
A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, South.
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?
R2= R=5.6 m/s
V=d/t m/s = 80m/t t=16s
V=d/t m/s=d/16s d=40m
5.59 m/s 16s 40 m

13. 3.
A boat is traveling across a river that flows due north at 12 m/s. The boat is moving at an angle 40 degrees west of north at a speed of 4 m/s with respect to the water. How fast and which way is the boat moving relative to the banks of the river?