1. Relative Motion

2. What is Relative Motion
Strictly speaking…all motion is relative to something.
Usually that something is a reference point that is assumed to be at rest (i.e. the earth).
Motion can be relative to anything…even another moving object.
Relative motion problems involve solving problems with multiple moving objects which may or may not have motion relative to the same reference point. In fact, you may be given motion information relative to each other.

3. Notation for Relative Motion
We use a combination of subscripts to indicate what the quantity represents and what it is relative to.
For example, “va/b” would indicate the velocity of “object a” with respect to “object b”. Object b in this example is the reference point.
Note: The “reference point” object is assumed to be at rest.

4. Example Problem
A plane flies due north with an airspeed of 50 m/s, while the wind is blowing 15 m/s due East. What is the speed and direction of the plane with respect to the earth?
What do we know?
“Airspeed” means the speed of the
plane with respect to the air.
“wind blowing” refers to speed of
the air with respect to the earth.
What are we looking for?
“speed” of the plane with respect to the earth.
We know that the speed and heading of the plane will be affected by both it’s airspeed and the wind velocity, so… just add the vectors.

5. Example Problem (cont.)
So, we are adding these vectors…what does it look like?
Draw a diagram,of the vectors tip to tail! Solve it!
This one is fairly simple to solve once it is set up…but, that can be the tricky part. Let’s look at how the vector equation is put together and how it leads us to this drawing. N θ

6. How to write the vector addition formula
middle
same
first
last
Note: We can use the subscripts to properly line up the equation. We can then rearrange that equation to solve for any of the vectors. Always draw the vector diagram, then you can solve for any of the vector quantities that might be missing using components or even the law of sines.

7. Displacement is relative too!
Other quantities can be solved for in this way, including displacement.
Remember that d=vt and so it is possible to see a problem that may give you some displacement information and other velocity information but not enough of either to answer the question directly
When solving these, be very careful that all the quantities on your diagram and in your vector formula are alike (i.e. all velocity or all displacement). Do not mix them!

8. 1 –D Relative motion
If car A is moving 5m/s East and car B, is moving 2 m/s West, what is car A’s speed relative to car B.
5 m/s
Car A
Car B
2 m/s
So, we want to know…if we are sitting in car B, how fast does car A seem to be approaching us? Common sense tells us that Car A is coming at us at a rate of 7 m/s.
How do we reconcile that with the formulas?

9. 1- D and the vector addition formula
Let’s start with defining the reference frame for the values given. Both cars have speeds given with respect to the earth.
Va/e =5 m/s
Car A
Car B
Vb/e = -2 m/s
We are looking for the velocity of A with respect to B, so va/b = ?
If we set up the formula using the subscript alignment to tell us what to add, we get…
Then we need to solve for va/b .
So…

10. Relative Motion It’s all about the reference point(s)
It’s all about the vectors
It’s all about common sense
Demos
Walking Demo: Me to you
Relative Motion Video
Car on Paper Demo 4:13

11. Relative Motion Amy, Bill, and Carlos are watching a runner.
The runner moves at a different velocity relative to each of them.
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12. Relative Velocity The runner’s velocity with respect to (wrt) Amy is
(vx)RA = 5 m/s
The subscript “RA” means “Runner wrt Amy.”
The velocity of Carlos wrt Amy is
(vx)CA=15 m/s
The subscript “CA” means “Carlos wrt Amy.”
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13. Question 1: Linear Motion
What is the velocity of the ball relative Mr A.
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14. Question 1: Linear Motion
What is the velocity of the ball relative Mr A.
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15. Question 2: What is the velocity of the ball relative to Mr. F.
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16. Question 2: What is the velocity of the ball relative to Mr. F.
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17. Question 3: What is the velocity of the ball relative to Mr. R.
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18. Question 3: What is the velocity of the ball relative to Mr. R.
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19. Question 4: Perpendicular Motion
a. How fast is the swimmer moving relative to Mr. B.
b. How long does it take the swimmer to get to the other side.
c. How far down the river does the current take the swimmer.
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20. Question 4: Perpendicular Motion
a. How fast is the swimmer moving relative to Mr. B.
b. How long does it take the swimmer to get to the other side.
c. How far down the river does the current take the swimmer.
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21. Question 5: Perpendicular Motion
a. What does the swimmer have to do to swim straight across the river?
b. How long will it take?
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22. Question 5: Perpendicular Motion
a. What does the swimmer have to do to swim straight across the river?
b. How long will it take?
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23. Question 6: Perpendicular Motion
A. What is the apparent velocity of the airplane to someone on the ground.
b. What should the pilot do so the plane goes to the north.
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24. Question 6: Perpendicular Motion
A. What is the apparent velocity of the airplane to someone on the ground.
b. What should the pilot do so the plane goes to the north.
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25. Question 1
A factory conveyor belt rolls at 3 m/s. A mouse sees a piece of cheese directly across the belt and heads straight for the cheese at 4 m/s. What is the mouse’s speed relative to (or wrt) the factory floor?
1 m/s
2 m/s
3 m/s
4 m/s
5 m/s
Answer: E
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26. Question 1
A factory conveyor belt rolls at 3 m/s. A mouse (he is on the belt) sees a piece of cheese directly across the belt and heads straight for the cheese at 4 m/s. What is the mouse’s speed relative to the factory floor?
1 m/s
2 m/s
3 m/s
4 m/s
5 m/s
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27. Question 2 Speed of a seabird
Researchers tracking of albatrosses in the Southern Ocean observed a bird maintaining sustained flight speeds of 35 m/s. This seems surprisingly fast until you realize that this particular bird was flying with the wind, which was moving at 23 m/s. What was the bird’s airspeed—its speed relative to the air? This is a truer measure of its flight speed.
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28. Question 2 Speed of a seabird
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29. Question 3 Finding the ground speed of an airplane
Cleveland is approximately 300 miles east of Chicago. A plane leaves Chicago flying due east at 500 mph. The pilot forgot to check the weather and doesn’t know that the wind is blowing to the south at 100 mph. What is the plane’s velocity relative to the ground?
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30. Question 3 Finding the ground speed of an airplane
Cleveland is approximately 300 miles east of Chicago. A plane leaves Chicago flying due east at 500 mph. The pilot forgot to check the weather and doesn’t know that the wind is blowing to the south at 100 mph. What is the plane’s velocity relative to the ground?
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31. Question 4
A skydiver jumps out of an airplane 1000 m directly above his desired landing spot. He quickly reaches a steady speed, falling through the air at 35 m/s. There is a breeze blowing at 7 m/s to the west.
At what angle with respect to vertical does he fall?
When he lands, what will be his displacement from his desired landing spot?
Answer: A: the angle of the skydiver with respect to the ground is the vector sum of 35 m/s down and 7 m/s to the west. The angle with respect to the vertical is ATAN(7/35)=11 degrees.
B: The skydiver moves horizontally at a constant speed of 7 m/s for the time it takes to fall. The vertical motion takes 1000/35 = 29 sections. The motion to the West is 1000/35*7=200 meters.
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32. Question 4
A skydiver jumps out of an airplane 1000 m directly above his desired landing spot. He quickly reaches a steady speed, falling through the air at 35 m/s. There is a breeze blowing at 7 m/s to the west.
Answer: A: the angle of the skydiver with respect to the ground is the vector sum of 35 m/s down and 7 m/s to the west. The angle with respect to the vertical is ATAN(7/35)=11 degrees.
B: The skydiver moves horizontally at a constant speed of 7 m/s for the time it takes to fall. The vertical motion takes 1000/35 = 29 sections. The motion to the West is 1000/35*7=200 meters.
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