Transcript ESS 303 -- Biomechanics

ESS 303 – Biomechanics
Projectiles
Which Will Hit First?
Y = 1/2 at2
Put Things Together (4 Steps)
 Step #1: Calculate the X and Y components of
movement.
 VX0 = V0 * Cos θ
 VY0 = V0 * Sin θ
 Step #2: Calculate the maximum height. How
far up did it go?
 Yup = (VY2 – VY02)/2a
 Ydown: How far down will it fall (think about it)?
Put Things Together (4 Steps)
Step #3: Calculate the hang-time
Y = ½at2
t = √(2Y)/a
Remember to add time up and time down
Step #4: Calculate the range (the
horizontal distance)
X = VX0 * t
A Shortcut?
v2Sin θCos θ + vCos θ√(vSin θ)2 + 2gh
R = ––––––––––––––––––––––––––––––––
g
Problems
You drop a penny
from the top of a
2000 meter-high
building
How long will it
take to hit the
ground?
How fast will it be
going when it hits?
Problems
A player kicked a football giving it a
velocity of 20m/s at an angle of 37°. It
was caught by another player at a height
of 1.5meters.
What were the X and Y components of
velocity?
How high did it go?
How long was it in the air?
How far apart were the players?
Quiz 2 Notes
Next week
Bring a calculator (with trig. functions)
Formula sheet provided (same as one on
the web)
Scratch paper is recommended
About 16 total points
About 5 problems ranging in points from
2 to 7
Show your work and include units
Quiz 2 Sample Problems
 A runner completes 17 laps of a quarter-mile
track. What was his or her distance and
displacement?
 Distance = 4.25 Miles
 Displacement = 0 Miles
 Move on a grid from point (3,6) to point (8,10).
What are your horizontal, vertical, and
resultant displacements?
 Horizontal Displacement = 5
 Vertical Displacement = 4
 Resultant Displacement = 6.40
More Quiz 2 Sample Problems
 A ballerina twirls 4½ times. What was her
angular distance in degrees and radians?
 Angular Distance = 1620 Degrees
 Angular Distance = 28.27 Radians
 While watching a golf swing, you note that the
angular velocity at the .18 second mark was
2.5 radians/second. You also see that the
angular velocity at the .41 second mark was
12.02 radians/second. What was the angular
acceleration?
  = (/t)
  = (12.02-2.5)/.41-.18) = (9.52/0.23) = 41.39 r/s2
Final Quiz 2 Sample Problem
A pitcher throws a ball 1.5 meters above
the ground. The ball is released at a 23
degree angle at a velocity of 37 m/s.
How far down-field will the ball go (do all
4 steps and show your work)?
37m/s
23º
Yup
YDown = Yup+1.5m
Final Quiz 2 Sample Problem
Step 1: Horizontal and Vertical Velocities
VX = (V0 * CosӨ)
VX = 34.06 m/s
VY = (V0 * SinӨ)
VY = 14.46 m/s
37m/s
23º
Yup
YDown = Yup+1.5m
Final Quiz 2 Sample Problem
Step 2: How high did it go (from point of
release)?
Y = (Vy02 – Vy12)/(2*a)
Yup = 10.66 meters
Ydown = 12.16 meters
37m/s
23º
Yup
YDown = Yup+1.5m
Final Quiz 2 Sample Problem
Step 3: What was the flight time?
t = √((2Y)/a)
tup = 1.47 seconds, tdown = 1.57 Seconds
ttotal = 1.47 + 1.57 = 3.04 Seconds
37m/s
23º
Yup
YDown = Yup+1.5m
Final Quiz 2 Sample Problem
Step 4: How far down-field did the ball
go?
X = VX * ttotal
X = (34.06 m/s * 3.04 s) = 103.54 meters
37m/s
23º
Yup
YDown = Yup+1.5m