Download Announcements Football Punter Physics

9/16/2011
Midterm Exam #1 Results
Announcements
• CAPA Set #4 due on Friday at 10 pm
Average = 77 out of 100
Std. Dev. = 15
• CAPA Set #5 due next Friday, now available in bins
• Next week in Section 
Assignment #3: Forces, Newton’s Laws, Free-Body Diagrams
Print out and bring the assignment to your section…
• Reading ahead in Chapter 4.1-4.6
(Forces and Force diagrams)
Specific letter grades are not assigned to individual
exams, and only a general range is indicated. 90-100 A
range, 80-90 B range, 65-80 C range, < 65 D/F range.
• Exam #1 grades posted on CULearn
Solutions for version #1 posted on CULearn
More details at “Exam Information” link and next slide
Solutions and grades posted on CULearn.
Exam booklets to be returned in Sections next week.
Football Punter Physics
x  x0  v0 x t  1 a x t 2
2
For a specific play, the punter wants
to kick the ball as far down the field
as possible (i.e. maximum range).
y  y0  v0 y t  1 a y t 2
2
x0  0

v0 x | v0 | cos 
y0  0

v0 y | v0 | sin 
ax  0
ay  g

y  (| v0 | sin  )t  1 gt 2
2

x  (| v0 | cos  )t
What is the optimal angle to
kick the ball at
assuming the same initial speed
when kicked regardless of the angle?
Football obeys the laws of physics.
Constant acceleration case (ignoring air resistance).
Approach
1. At what time (t) does
the ball hit the ground
(i.e. when is y=0)
2. Then evaluate the x
position at that time
(thus giving the Range)

Room Frequency BA
Clicker Question

x  (| v0 | cos  )t

y  (| v0 | sin  )t  1 gt 2
2

x  (| v0 | cos  )t

y  (| v0 | sin  )t  1 gt 2
2
Time of football flight (i.e. hang time)

t  2(| v0 | sin ) / g


Clearly at t =0, x=0 and y=0
(our initial conditions).
At what later time does the football hit the ground?
A)
B)
C)
D)
E)
t = 10 seconds
t = |v0| tan
t = Sqrt(2|v0|sin/g)
t = 2|v0|sin/g
None of the above

0  (| v0 | sin  )t  1 gt 2
2

0  t (| v0 | sin  )  1 gt
2

(| v0 | sin  )  1 gt  0
2

t  2(| v0 | sin ) / g


Now plug into x-equation to find out position when it hits the ground.


x  (| v0 | cos  )2 | v0 | sin / g 
x

2 | v0 |2 cos  sin 
g


| v0 |2 sin 2
g
* Uses trigonometry identity 2cossin=sin2
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9/16/2011
http://www.nflrush.com/video/science-of-nflfootball/1711
NFL Punter Craig Hentrich
- Over 100 NFL punts
- Often kicks ball at over 90 miles/hour
- Often kicks ball over 120 feet into the air

| v |2 sin 2
x( Range)  0
g
sin(2) versus 
He says in the video that one tries to kick the ball to keep
it in the air as long as possible.

What angle  gives the
t ( HangTime)  2(| v0 | sin ) / g
longest hang time?
 2
| v0 | sin 2
 = 90 degrees
x( Range) 
g
What angle  gives the
longest distance range?
 = 45 degrees
What do Punters Really Do?
http://www.livestrong.com/article/510672-angles-affecting-a-punt-in-football
The Kicker's Dilemma
Calculations shows that the maximum horizontal range of the punt is achieved by
kicking it at a 45-degree angle, but such a kick has a hang time -- football terminology
for time spent in the air -- almost 30 percent less than the theoretical maximum for a
given launching speed.
Meanwhile, the maximum theoretical hang time occurs with a kick straight up at 90
degrees, but such an angle would be nonsensical given the goal of sending the football
down the field.
Typical Launching Angle
After analyzing 238 punts by NFL kickers, one finds an average launch speed of 60 to 70
mph, an average hang time of about 4.1 seconds and a typical launching angle from
55 to 60 degrees. Punters may drop below 50 degrees to gain more distance or go as
high as 70 degrees to increase hang time.
http://en.wikipedia.org/wiki/Range_of_a_projectile
We now know some of the basics about how
objects move under constant acceleration.
Kinematics.
We now want to know why what causes these
accelerations (forces).
Dynamics
By launching a punt at a 55-degree angle instead of 45 degrees,
the punter loses about five yards of distance and
gains more than half a second of hang time.
Dynamics: Newton’s Laws of Motion
Isaac Newton: 1643-1727
English physicist, mathematician, astronomer,
natural philosopher, alchemist, and theologian.
1687: Philosophiæ Naturalis Principia
Mathematica.
Newton described universal gravitation and
the three laws of motion.
Showed that the motion of objects on Earth and of
celestial bodies are governed by the same set of natural
laws, thus removing the last doubts about
heliocentrism and advancing the scientific revolution.
Dynamics: Newton’s Laws of Motion
Mechanics:
Three laws.
Conservation laws: momentum, angular momentum.
Gravitation. (Coined the term “gravity”.)
Optics:
Built the first "practical" reflecting telescope.
Developed a theory that white light is
composed of different wavelengths of light.
Mathematics:
Invented the calculus (with Leibniz).
Biblical hermeneutics:
Wrote many religious tracts.
Alchemist: Pb  Au
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9/16/2011
Excellent biography of Newton.
Very interesting insight on character.
Reminds one why they called
it Philosophy back then.
Newton’s Three Laws
Newton’s Laws (as stated) hold in an
“Inertial Reference Frame” (non-rotating / non-accelerating):
I. “Law of Inertia”: Every object continues in its state
of rest, or uniform motion (constant velocity in a
straight line), as long as no net force acts on it.
II. Acceleration is proportional to force and inversely
proportional to mass. Famous F net  ma equation.
III.Whenever one object exerts a force on a second
object, the second exerts an equal force in the
opposite direction on the first.
F AB  F BA
Newton’s First Law
Cases with very, very little friction demonstrate this physics.
Every object continues in its state of rest,
or of uniform velocity in a straight line,
as long as no net force acts on it.
Ancients believed either that rest (terrestrial bodies) or circular
motion (celestial bodies) was the natural state of objects.
An object moving at some velocity usually slows down to a stop,
and thus it seemed that rest was the natural state.
In fact, Gallileo thought that this was not true and that without
friction or air resistance an object in motion would simply continue
in motion. Newton liked this idea.
Clicker Question
Room Frequency BA
An astronaut in intergalactic space is twirling a rock on a string.
Suddenly the string breaks when the rock is at the point shown.
http://en.wikipedia.org/wiki/Curling
Clicker Question
Room Frequency BA
A glider (Yoda) is gliding along an air track at constant speed.
There is no friction and no air resistance.
Which path (A, B, C, or D) does the rock follow after the string breaks?
At the point indicated the rock has
a velocity vector to the right.
When the string breaks, there are
no more forces acting on the rock.
According to Newton's first law, the
rock must move with constant
velocity in a straight line.
What can you say about the net force (total force) on the glider?
A) The net force is zero.
B) The net force is non-zero and is in the direction of motion.
C) The net force is non-zero and is in the direction opposite the
motion.
D) The net force is non-zero and is perpendicular to the motion.
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