problemSet2-Fa23-KEY (1)
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School
University of Massachusetts, Amherst *
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Course
430
Subject
Health Science
Date
Dec 6, 2023
Type
Pages
6
Uploaded by DeaconFlyMaster905
KIN 430 – Problem Set 2
1
KIN 430 – Biomechanics
Fall Semester 2023
Problem Set #2 (25 points) – Due on Wednesday, Oct 11th, 2023 by 5pm.
To receive full credit, you must hand the completed problem set directly to one of the course instructors
or have the KIN front office time stamp and place in Dr. Boyer’s mailbox prior to 5pm on Wednesday (do
not slip it under a door or leave it in the front office)
Complete this problem set by printing and placing your answers in the spaces provided. Do all your calculations
within the margins or on separate sheets of paper, clearly indicating which calculations go with which problem.
Staple any separate sheets of paper to this problem set before you turn it in to receive full credit.
You must show
your calculations to receive full credit, even if you have the correct answers
. Don’t forget to include proper
SI
units
!
1. (4 pts.)
Usain Bolt currently holds the World record time in the 100 m sprint of 9.58 s. Here are the World
record times for three prominent former World record holders: Donald Lippincott 10.60 s (1912); Jesse Owens
10.20 s (1936); Carl Lewis 9.86 s (1991). Assuming that in a head-to-head race each athlete ran the whole race
at their average World record velocity, how many meters behind Usain Bolt would the three former World
record holder finish?
For giggles, let’s add in a regular human for comparison. Abby threw the javelin and discus in college but was
forced to run the 100 m one meet and ran it in 14.40 s. How far behind Bolt would Abby have finished?
Lippincott: meters behind Bolt: __________
Owens: meters behind Bolt:
__________
Lewis: meters behind Bolt:
__________
Abby: meters behind Bolt:
__________
9.66m
GRm
2.86m
Vw
33.51m
ds
Varg
time
Lippincott
10
601
baugs.IQ
a.s9.43mbds9.43mis
9.584
90.34
100
9034
9.66m
Owens
10.20
bangs
1
7
9180Mt
d
918019.587
93.88
100
93.886.12m
Lew
9.86
Varg
4
7
10
14mi
d
101469.587
97.14
100
97.14
7.86
Abby
14.40
Varg
Yg
6.94mi
d
6.94
9,587
66.485
100
66.485
33.51m
KIN 430 – Problem Set 2
2
2. (2 pts.)
The average human head cannot tolerate accelerations of greater than about 30 g’s (g-force; 1g =
9.81m/s
2
) without sustaining serious injury, such as concussion. Protective helmets, as worn in football or by
cyclists, work in part by increasing the time over which a rapid deceleration of the head happens, so as to reduce
the magnitude of the acceleration. Consider a football player whose head was initially moving at 21 m/s and then
suddenly stopped due to a collision with another player. What is the
minimum
amount of time over which the
deceleration of his head can occur, such that the magnitude of the acceleration that his head experiences is
not
greater than 30 g’s?
Minimum time over which the athlete’s head can safely decelerate _____________
4 21,1
95981
30
2943,19071s
a
VfI
if
O
2.94.3
0
t
t
0.07135
KIN 430 – Problem Set 2
3
3.
(4 pts.)
In a recent golf match, Brooks Koepka had to hit his ball up onto a green that was located 3.5 m above
the point from which he was hitting the ball. If the ball left his club with a velocity of 22.5 m/s at an angle of
55 deg above the horizontal, how long did it take for the ball to first hit the ground, and how far did it travel
during that time? (Ignore the effects of air resistance)
Time for the ball to first hit the ground?
________________
Distance the ball travels before hitting the ground? (d
H
in the figure below) ________________
Ball first hits
ground here
d
H
ball
3.5 m
θ
= 55
°
v = 22.5 m/s
3.56sec
45.4M
Siritikat
the
flow
22.5955
18,43
mi
Y'titat
22.5
a55
12.905mi
Eup
18.431
9.81
1114
ta
teams
13.81
4.90515
1.6787yd
1.879
it
9055
18
net
3.5
0
e
006,3557
due
17.31m
Eggs
1,879
1,678
3.557
downs
17.31
3.5
13.81
m
for
total
hozdistma
d
vet
4
12.905
3.557
45.90J
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KIN 430 – Problem Set 2
4
4.
(
6 pts.)
Skylar is preparing preliminary data for her dissertation proposal.
She is interesting in determining
how individual with knee OA change their gait in response to muscle fatigue.
Following her data collection, Dr.
Boyer asked Skylar what the Thigh, Leg, and Foot segments angles were at toe-off.
And while she was at it, what
were the Knee and Ankle joint angles.
Unfortunately, Skylar had not calculated these angles yet. She did however
have marker positions for the right greater trochanter, lateral knee joint, lateral ankle joint, and toe from his
experience.
At toe-off, these markers positions (x=horizontal, y=vertical) were (610, 805), (520, 440), (250, 125),
and (380, 0), respectively in mm.
So, Dr. Boyer asked her to calculate Thigh, Leg and Foot segment angles and
knee and angle joint angles from those marker positions and to identify whether the knee joint is flexed or
extended, and whether the ankle joint is dorsiflexed or plantar flexed, relative to the anatomical position (use the
convention defined in the class slides and KIN 430 textbook on pages 321-325).
If Skylar plans to graduate, what
angles should she report back to her committee?
Thigh Segment Angle ___________
Leg Segment Angle
___________
Foot Segment Angle
___________
Knee joint angle
____________
Flexed or Extended
______________
Ankle joint angle
____________
Dorsiflexed or Plantar Flexed ______________
76.150
49.400
3
280
flexed
dorsi
flexed
leg
0520,440
t
8
go.is
y
as
tail
49.3990
É
amount
tailfo
43.880
waffles
ta
8
76.15
II
away
µ
t
G
knee
Othinh
G
shark
76.15
49.40
Garth
Gley
Afoot 90
49.4
136.12
90
3.280
KIN 430 – Problem Set 2
5
5. (4 pts.)
Monica Abbot holds the world record for fastest softball pitch, clocking in at 77mph.
If we make the
rather brazen assumptions that this velocity represents the ball’s tangential velocity at release, that velocity was
all generated by her shoulder joint, her shoulder rotational velocity was constant around release, and her arm was
rigid and measured 63.5cm from shoulder joint to the ball center. What was her arm tangential velocity (m/s),
angular velocity, tangential acceleration, and radial acceleration at release during this record setting pitch?
Tangential velocity of ball (in m/s):
____________
Shoulder angular velocity:
____________
Tangential acceleration of the ball:
____________
Radial acceleration of the ball:
____________
u.int
O
n
Is
So
All
a
1865.73
m
1
Vt
77
mph
34.42m
my
Ven
w
a
s
d
e
r
34.42
0.635
W
9
s
0
635
0
1
a
Y
9
5,1
1865.73
mm
KIN 430 – Problem Set 2
6
6.
(5pts)
Wakaba Higuchi is a Japanese Figure Skater and one of the 10 athletes in the Women’s singles figure
skating competition to ever land a triple axel in Olympic competition.
A Triple axel consists of three and one
half rotations in the air.
If she takes off with a velocity of 5.92m/s at 38 degree angle, how quickly does she
need to rotate to complete all 3.5 rotation in the air before landing?
total
rotations
360
3.5
1260
need
to
find
time
n
ai
5.925in
38
3.645
Vf
Vit
at
tf
so
at
top
O Vit
9.8
t
y
W
Ft
6
44
1693
0
3.645
9.8
t
3.645
9.814
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