1. Two-Dimensional Motion and VectorsSection 1 Preview Section 1 Introduction to VectorsIntroduction to Vectors Section 2 Vector OperationsVector Operations Section 3 Projectile MotionProjectile Motion Section 4 Relative MotionRelative Motion

2. Section 4Two-Dimensional Motion and Vectors Click below to watch the Visual Concept. Visual Concept Relative Motion

3. Section 4Two-Dimensional Motion and Vectors Frames of Reference A falling object is shown from two different frames of reference: –the pilot (top row) –an observer on the ground (bottom row)

4. Two-Dimensional Motion and VectorsSection 4 Relative Velocity v ac = v ab + v bc –v ac means the velocity of object “a” with respect to frame of reference “c” –Note: v ac = -v ca When solving relative velocity problems, follow this technique for writing subscripts.

5. Section 4Two-Dimensional Motion and Vectors Sample Problem A boat is traveling downstream. The speed of the boat with respect to Earth (v be ) is 20 km/h. The speed of the river with respect to Earth (v re ) is 5 km/h. What is the speed of the boat with respect to the river? Solution: v br = v be + v er = v be + (-v re ) = 20 km/h + (-5 km/h) v br = 15 km/h

6. Two-Dimensional Motion and VectorsSection 4 Classroom Practice Problem A passenger at the rear of a train traveling at 15m/s relative to the earth throws a baseball with a speed of 15m/s in the direction opposite the motion of the train. What is the velocity of the baseball relative to Earth as it leave the thrower’s hand? Answer: 0 m/s

7. Two-Dimensional Motion and VectorsSection 4 Classroom Practice Problem A spy runs from the front to the back of an aircraft carrier at a speed of 3.5m/s. If the aircraft carrier is moving forward at 18,0 m/s, how fast does the spy appear to be running when viewed by an observer on a nearby stationary submarine? Answer: 14.5 m/s in the direction that the aircraft carrier is moving

8. Two-Dimensional Motion and VectorsSection 4 Classroom Practice Problem A ferry is crossing a river. If the ferry is headed due north with a speed of 2.5m/s relative to the water and the river’s velocity is 3.0m/s to the east, what will the boat’s velocity be relative to the Earth? (Remember to include the direction in describing the velocity Answer: 3.9 m/s at 40.0° north of east

9. Two-Dimensional Motion and VectorsSection 4 Classroom Practice Problem A passenger at the rear of a train traveling at 15m/s relative to the earth throws a baseball with a peed of 15m/s in the direction opposite the motion of the train. What is the velocity of the baseball relative to Earth as it leave the thrower’s hand? Answer: 565.0 km/h at 40.1° north of east

10. Two-Dimensional Motion and VectorsSection 4 Classroom Practice Problem A pet store supply truck moves at 25.0m/s north along a highway. Inside, a dog moves at 1.75 m/s at an angle 35.0° east of north. What is the velocity of the dog relative to the road? Answer: 26.4 m/s at 2.17° east of north

11. Section 4Two-Dimensional Motion and Vectors Now what do you think? Suppose you are traveling at a constant 80 km/h when a car passes you. This car is traveling at a constant 90 km/h. –How fast is it going, relative to your frame of reference? –How fast is it moving, relative to Earth as a frame of reference? Does velocity always depend on the frame of reference? Does acceleration depend on the frame of reference?