To run or walk???
Physics of 2D Motion
September 20, 2010

• Administration
• Key Concepts – Physics 2D motion
• Relative Motion

• Homework Assignments
– Due Tuesday, Online lab homework
– Due Sunday, Written homework, & Ch. 4 Online homework
• Help Sessions – T/TH 8-9pm
• View Jupiter – Tonight 9 pm, Merrill Beach

• Let’s say you have a velocity vector that is 6 mph at 55 degrees relative to the x axis. What is the component of the vector along x?
– A) 6cos(55 degrees)
– B) 6sin(55 degrees)
– C) 6/sin(55 degrees)
– D) 6tan(55 degrees)
6 mph
?

• If you add vector 1 (5 at 37 degrees) to vector
2 (2 at 0 degrees), what do you get for the component in the x direction?
– A) 5
– B) 4
– C) 6
– D) 7

• v=at+v
0
, what does x=?
– x=(1/2)at 2 +v
0 t+x
0

• When you throw a ball up, at max height, acceleration in y is? (-9.8 m/s 2 )
• When you throw a ball up, at max height, velocity in y is?
(0 m/s)
• A car goes from 0 to 4 m/s in 0.5 s. What is the car’s acceleration?
(8 m/s 2 )

Usain’s Position vs. time
Except between time
0 s to 1.89 s, Usain has a constant velocity of ~10 m/s
Usain’s acceleration = 0 m/s^2

Position vs. time for two flies
Each dot is a position at 20 Hz
Velocity vs. time and acceleration vs. time is more complicated than Usain Bolt

• 2D Motion
– Independent in x and y
– Constant acceleration
• Relative Motion
• Projectile Motion

• Motion in x and motion in y is independent
– Separate into motion in x and motion in y
– Use the equations of motion for 2D to solve for unknowns
– Separate and Solve
• Most problems will assume constant acceleration
– Equations of motion?

X
I.
v x
 v
0 x
 a x t
II.
x

III.
v x
2 x

0
 v
0 x t
 v
0
2 x a x t
2
2

2 a x
( x
 x
0
)
Y
I.
v y
 v
0 y
 a y t
II.
y
III.
v y

2 y

0 v
0
2
 v
0 y t
 y a y t
2
2

2 a y
( y
 y
0
)

• Relative motion – motion of a frame that an object is moving in
• Motion of object in frame is just equal to object’s motion
• Motion of object out of frame is equal to object’s motion + frame motion
 v relative
 v
 object
 v
 frame

Relative Motion – Walkway at Airport
• I am running at 2 m/s in the airport and the moving walkway is at 3 m/s. If I take the walkway what is my speed?
– 5 m/s
• Do I take the walkway or run if there is a family on walkway so that I can’t run on it?
– take walkway
• If I just run the 10 m to the gate instead of taking the walkway will I still beat my brother who is going 3 m/s and is 11 m behind me?
– yes

• A river has a current of 3 m/s. A boat pointed straight across the river with a speed of 4 m/s appears from the shore to have a velocity of what value?
4 m/s
3 m/s

• A river has a current of 3 m/s. A boat pointed straight across the river with a speed of 4 m/s appears from the shore to have a velocity of what value?
– 5 m/s at an angle of 40 degrees from the shore

• A bucket is left out in the rain. The rain is coming down at 5 m/s. If a crosswind starts to blow at 2 m/s, will the bucket fill faster or slower?
5 m/s Original rain
5 m/s
Wind at
2 m/s
Scenario #1
Scenario #2

Relative Motion – Run or Walk in Rain?
• Is it better to run or walk in the rain?

Relative Motion – Run or Walk in Rain?
• Is it better to run or walk in the rain?
– Assume rain is coming straight down at 1 m/s
– If you run at 2 m/s, what does the rain look like in your frame?
• looks like coming at you instead of straight down
– If you just look at surface area of body getting wet, does walking or running hit less surface area?
• Walking
– If you look at how many rain drops hit you, does walking or running have less total rain drops?
• Running because you reach your destination sooner

• Separate 2D motion into x and y and then solve
• Use Kinematic equations of Motion to solve for problems with constant acceleration
• Relative Motion – make sure to add velocity of frame to velocity of object to get relative velocity