PHYS 218: General Physics
Summer 2013
Lecture 8:
More 2D Crap…
Just Kidding
Read: Ch. 5.1 – 5.3
Something moving horizontally
Free body diagram

Fgrav  mg

F
m

a
ay  g
The point is x and y are completely decoupled
here. The x-direction follows constant velocity,
regardless of the fact that the ball is falling.
Similarly, the object moves in y-direction just
as it would had it been simply dropped.
How to solve a 2D problem:
• First draw picture
• Then break into x
and y components
• Write down what
you know and want
• Choose equation
• Solve
q
v
vy = v sin q
vx = v cos q
Question
An object is fired from a cannon with an
initial speed of 100 m/s at an angle of
30o. After 3 seconds has it hit the
ground?
v0
q  30o
A. Yes
B. No
Shoot the Monkey
You fire the cannon. The monkey sees the flash
and lets go to avoid the cannon ball. What
angle should you set to hit the monkey?
A. <q
B. q
v0
q
C. >q.
Why?
In the absence of gravity, the monkey
would hang there and the ball would
follow the straight trajectory. Adding
gravity to this causes both the monkey
and the ball to accelerate at exactly the
same rate.
v0
q
More violent physics
You want to shoot the cannon as far
as possible (to avoid the other guy’s
guns). What q should you use?
q
Trade-off between loft and
forward velocity
q  90 deg
Lots of loft
No forward velocity
q  0 deg
Lots of forward velocity
no loft
Use independence of x and y
x-component is easy. No forces
means constant velocity
xlands  v x , 0t
q
xlands
Use independence of x and y
t is found by figuring out how long it
would take the initial vy to become
-vy.

v vy ,0v0v yat
, 0  gt
t
2v y ,0
g
q
xlands
Putting it together
xlands  v x , 0t
t
2v y ,0
g
2
2
2v
v
xlands 
cos q sin q  sin( 2q )
g
g
q
xlands
Easiest way to find maximum
q max  45 degrees
q
xlands
The red curve is the drag-free case. What would
the trajectory look like with same initial angle and
velocity but in the presence of air drag?
The red curve is the drag-free case. What would
the trajectory look like with same initial angle and
velocity but in the presence of air drag?
Reference Frames
Important for settling arguments.
Newton’s Laws gives consistent
results when applied from any
reference frame moving at
constant velocity.
You can put the origin of the coordinate system
at any location and Newton’s Laws still work
A ball drops from a desk at a height of 3 m. What is the time
required to reach the ground?
1 2
y  y0  v y ,ot  at
2
1 2
 y0  gt  t 
2
y
2 y0  y 
g
x
3m
Origin on desk
y
y0  0
x
y  3 m
Origin on floor
y0  3 m
y0
Either way Newton’s Laws predict same t
Newton’s Laws even work with an origin moving at constant velocity
30 mph
y
On
truck
70 mph
x
60 mph
y
On
ground
x
(a) Acceleration of Cheetah viewed on ground
v  v 60  (70)mph
f
i
a

 0.018mile / s 2
t
2s
(b) Acceleration of Cheetah as viewed on truck
v  v 100  (30)mph
f
i
a

 0.018mile / s 2
t
2s
Reference Frames
In any inertial reference frame
you agree on accelerations
and therefore forces present.
inertial reference frame: a
reference frame moving at
constant velocity
Quiz
You are flying a 1957 Cessna 172 (top
speed 150 mph) from Corpus Cristi to
Minneapolis. Winds are easterly at 30
mph. Ballpark an appropriate heading.
A.
B.
C.
D.
W
WNW
NNW
N
N
Minneapolis
E
W
Corpus
Christi
S
For Next Time
Read Chapter 5.1-5.3
Quiz 5 (Prelude to circular motion)
You peg the speedometer at constant speed 70 mph and
whizz around a curved on-ramp. Are you accelerating?
A. Yes
B. No
Quiz 5 (Prelude to circular motion)
vx ~ 0
vy ~ v
vx ~ -v
vy ~ 0
You peg the speedometer at constant speed 70 mph and
whizz around a curved on-ramp. Are you accelerating?
A. Yes
B. No
Quiz 5 (Prelude to circular motion)
vx ~ 0
A vchange
y ~ v
vx ~ -v
in direction produces an
vy ~ 0
acceleration. That’s why you feel a force
when you drive around a curve.
You peg the speedometer at constant speed 70 mph and
whizz around a curved on-ramp. Are you accelerating?
A. Yes
B. No