problemSet2-Fa23-KEY (1)

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University of Massachusetts, Amherst *

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430

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Health Science

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Dec 6, 2023

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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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