Projectiles are covered in the projectile super problem. See lectures link.
A summary of how to add vectors by using components is on the lectures link.
Relative velocity is a great example of adding vectors.
Have you ever had this happen to you? While sitting in your car at a red traffic light, the car
beside you slowly drifts forward. You mash on the brake to stop your car from rolling
backwards, but your car is not moving.
Within your environment, there is no way to distinguish between your car moving backwards
and the car besides you moving forward. The velocity is relative. We need a reference frame
(the traffic light, for example) to define who is moving.
The train moves at 10 m/s and Wanda can walk at 1 m/s. How fast will Greg see Wanda walk?
Wanda’s velocity relative to Greg is the sum of the velocity of the Wanda relative to the train
plus the velocity of train relative to Greg.



vWG  vWT  vTG
Notice the order of the subscripts. We have the Ts cancelling from the two terms on the right.
This equation will always hold, but how do we use it? What is our rule about vectors?
WE DO NOT DEAL WITH VECTORS. WE DEAL WITH THEIR COMPONENTS.
Take the x-component:
vWGx  vWTx  vTGx
 (1m/s)  (10 m/s)
 11m/s
Greg sees Wanda walking to the right at 11 m/s. What happens when she walks back to her seat?
vWGx  vWTx  vTGx
 (1m/s)  (10 m/s)
 9 m/s
According to Greg, Wanda is walking at 9 m/s to the right.
Hopefully, this is pretty easy. But what about this?
From Example 3.11. Jack wants to row directly across the river from the east shore to a point on
the west shore. The current 0.60 m/s and Jack can row at 0.90 m/s. What direction must he
point the boat and what is his velocity across the river?
The velocity of the rowboat relative to the shore is equal to the velocity of the rowboat relative to
the water plus the velocity of the water relative to the shore.



v RS  v RW  vWS
The rowboat is to head directly to the west.
Take components.
vRSx  vRWx  vWSx
and
vRSy  vRWy  vWSy
The diagram is the key to solving relative velocity problems. For the x-component,
vRSx  vRWx  vWSx
vRS  vRW cos  0
 vRW cos
The y-component,
vRSy  vRWy  vWSy
0  vRW sin  vWS
vWS  vRW sin
Our unknowns are  and vRS. From the y-component equation,
vWS  vRW sin
sin 

vWS
vRW
0.6 m/s
0.9 m/s
 0.667
  41.8
From the x-component equation.
vRS  vRW cos
 (0.90 m/s) cos 41.8
 0.67 m/s
The boat must point 41.8º N of W upstream. Its speed across the water is 0.67 m/s.
A more general problem will occur as a super problem.
Now to Chapter 4 (the good stuff)
We can describe motion, but why do things move?
Forces: Objects interact through forces. “A force is a push or pull.” Forces can be long range
(gravity, electric, magnetic, etc.) or contact (normal force, tension, etc.).
Fig. 04.01
Obviously, forces are vector quantities since their effect depends on the direction of the force.
The net force is the vector sum of all forces acting on an object.

  

Fnet   F  F1 F2    Fn
A free-body diagram (FBD) is an essential tool for finding the net force acting on an object.
(See page 91.)
 Draw the object in a simplified way
 Identify all the forces that are exerted on the object.
 Draw vector arrows representing all the forces on the object.
Examples
1. Freely falling object.
2. Object hanging from a rope.
3. Object sitting on a horizontal table.
4. Object sitting on a horizontal table being pulled by a rope.
FREE BODY DIAGRAMS GO HERE. I will draw them on the board.
Drawing the free-body diagram is the key to solving problems.

Newton’s First Law (law of inertia): An object’s velocity vector v remains constant if and only
if the net force acting on the object is zero.
A object moving at constant velocity has no net force! A revolutionary idea.
An object moving at constant velocity is said to be in translational equilibrium. That velocity
could be zero.
Inertia is the resistance to changes in velocity.
Newton’s Second law: The rate of change of an object’s velocity is proportional to the net force
acting on it and inversely proportional to its mass.


 F ma
Recall our rule: we never deal with vectors, we deal with their components. A far more useful
form of Newton’s second law will be
F
x
ma x
F
y
ma y
The left hand side is supplied by the free-body diagram. The right hand side is supplied by our
knowledge of the motion.
The SI unit of force is the newton. 1 N = 1 kg·m/s2.
What is mass? Mass is a measure of inertia. Mass is not the same as weight.
Newton’s Third Law: In an interaction between two objects, each object exerts a force on the
other. These forces are equal in magnitude and opposite in direction.
It two objects A and B are exerting forces on each other,
A
FBA
B
FAB


FAB  FBA
The forces are equal in magnitude and opposite in direction.