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KINE 3030 Mock Midterm 1. A boat travels west at 50km/h 30 minutes before heading Southeast for at 40km/h 1 hour. What was the boat’s displacement in km? a) 31.41 b) 28.47 c) 38.37 d) Cannot be determined 2. A schoolgirl is completing a cartwheel. She is rotating about the ________ axis and moving along the ________ plane. a) frontal, sagittal b) frontal, transverse c) sagittal, frontal d) sagittal, transverse 3. When turning one’s head left and right, there is movement along the ______ plane. a) sagittal b) transverse c) frontal d) coronal 4. An alien has a mass of 200 kg on Earth. What is the alien’s mass on Jupiter which has a gravity of 24.79 m/s^2? a) 1962 N b) 2958 N c) 8.068 N d) None of the above 5. Which of the following is an example of a vector? a) torque b) distance c) weight d) gravity e) Two or more of the above are vectors f) All of the above are vectors 6. A blue ball is thrown parallel to the ground at a speed of 90 km/h on a platform that is 5 m above ground level. At the same time, a red ball is also thrown parallel to the ground at a speed of 50 km/h on a platform that is 4 m above ground level. Which ball will hit the ground first? a) The blue ball b) The red ball c) Both will hit the ground at the same time d) Cannot be determined 7. A torque of 20 N.m is applied by a wrench. Assuming the force was applied 30cm from the bolt, how much force was applied? a) 66.66 N

b) 6.66 N c) 600 N d) 6 N 8. A 75 kg man is measuring his weight on a scale that is 30cm wide and 30cm long. How much pressure is being applied on the scale? a) 8175 kPa b) 8.175 kPa c) 0.8175 kPa d) 735.75 Pa 9. A student throws a baseball and it hits the ground 30m away. When is the vertical velocity at its greatest? (assuming the projection and landing heights are the same and neglecting air resistance) a) Just after the start of the throw b) When the ball is 15m away horizontally c) Just before the ball hits the ground d) Two of the above e) All of the above 10. A student throws a baseball and it hits the ground 30m away. When is the horizontal velocity at its greatest? (assuming the projection and landing heights are the same and neglecting air resistance) a) Just after the start of the throw b) When the ball is 15m away horizontally c) Just before the end of the throw d) Two of the above e) All of the above 11. A basketball is rolling along the ground with a velocity of 10 m/s and stops after rolling for 7.5 seconds. At what is the basketball accelerating? a) 1.33 m/s b) 2.50 m/s c) -1.33 m/s d) -2.50 m/s 12. Which of the following is an example of a quantitative absolute angle? a) Measuring the angle between one’s humerus and radius/ulna b) Measuring the angle between one’s femur and tibia c) Measuring the angle of the tibia with respect to the floor d) A and B are true 13. A 50 kg woman is standing on a 0.15m by 0.3m scale. What is the weight of the woman? a) 10900 Pa b) 1.09 kPa c) 490.5 N d) 4905 N

14. A diver is spinning in midair at 15 rad/s and stops upon hitting the water. Assuming she starts spinning as she begins her dive, and hits the water 4 seconds after beginning her dive, what was the diver’s angular acceleration? a) 3.75 rad/s/s b) -3.75 rad/s/s c) 60 rad/s/s d) Cannot be determined 15. An individual is performing a bicep curl. Which of the following planes is the most appropriate for viewing the motion? a) Sagittal plane b) Frontal plane c) Transverse plane d) None of the above are appropriate 16. When attempting to estimate one’s neuromuscular activation, they would use an ________. When attempting to estimate one’s ground reaction force, they would use ________. a) force plates, EMG b) EMG, force plates c) force plates, force plates d) handgrip dynamometer, force plates 17. A father takes 15 minutes to drive his son from their home to York, 10 km away. The father then drives back home in 10 minutes. When he arrives back home, what was his average velocity over the trip? a) 40 km/h b) 48 km/h c) 0 km/h d) Cannot be determined 18. The wheels of a car are turning at a constant angular velocity of 12 m/s relative to their axles over a period of 12 seconds. What are the wheel's angular acceleration? a) 1 rad/s/s b) 12 rad/s/s c) 0 rad/s/s d) Cannot be determined 19. You are standing on a flat soccer field and are trying to throw a ball as far as you can. Assume you throw the ball with the same force, which of the following projection angles would be best for throwing it the furthest distance? a) 30 degrees b) 45 degrees c) 60 degrees d) It does not matter what angle you throw it at 20. Assume a car is moving at 20 m/s and is approaching a yellow light. The driver presses their breaks and comes to a stop to a stop after 4 seconds. What is the car’s acceleration over the breaking period? a) 20 m/s/s b) 5 m/s/s

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c) 0 m/s/s d) None of the above 8. Solve for x in each of the equations below. Refer to Appendix A for help if necessary. a. x = 5 3 b. 7 + 8 = x /3 c. 4 × 3 2 = x × 8 d. −15/3 = x + 1 e. x 2 = 27 + 35 h. 7 × 5 = −40 + x i. 3 3 = x /2 j. 15 − 28 = x × 2 (Answers: a. 125; b. 45; c. 4.5; d. −6; e. 7.9; f. 8.9; g. 3.2; h. 75; i. 54; j. −6.5) 9. Two schoolchildren race across a playground for a ball. Tim starts running at a distance of 15 m from the ball, and Jan starts running at a distance of 12 m from the ball. If Tim’s average speed is 4.2 m/s and Jan’s average speed is 4.0 m/s, which child will reach the ball first? Show how you arrived at your answer. (See Sample Problem 1.1.) (Answer: Jan reaches the ball first.) 10. A 0.5 kg ball is kicked with a force of 40 N. What is the resulting acceleration of the ball? (Answer: 80 m/s 2 ) ADDITIONAL PROBLEMS 1. Select a specific movement or sport skill of interest, and read two or three articles from the scientific literature that report the results of biomechanical investigations related to the topic. Write a short paper that integrates the information from your sources into a scientifically

based description of your chosen movement. 2. When attempting to balance your checkbook, you discover that your figures show a different balance in your account than was calculated by the bank. List an ordered, logical set of procedures that you may use to discover the error. You may use list, outline, or block diagram format. 3. Sarah goes to the grocery store and spends half of her money. On the way home, she stops for an ice cream cone that costs $0.78. Then she stops and spends one-fourth of her remaining money to settle a $5.50 bill at the dry cleaners. How much money did Sarah have originally? (Answer: $45.56) 4. Wendell invests $10,000 in a stock portfolio made up of Petroleum Special at $30 per share, Newshoe at $12 per share, and Beans & Sprouts at $2.50 per share. He places 60% of the money in P.S., 30% in N, and 10% in B & S. With market values changing (P.S. down $3.12, N up 80%, and B & S up $0.20), what is his portfolio worth six months later? (Answer: $11,856) 5. The hypotenuse of right triangle ABC (shown here) is 4 cm long. What are the lengths of the other two sides? (Answer: A = 2 cm; B = 3.5 cm) 6. In triangle DEF , side E is 4 cm long and side F is 7 cm long. If the angle between sides E and F is 50 degrees, how long is side D? (Answer: 5.4 cm) 7. An orienteer runs 300 m north and then 400 m to the southeast (at a 45° angle to north). If he has run at a constant speed, how far away is

he from the starting position? (Answer: 283.4 m) 8. John is out for his daily noontime run. He runs 2 km west, then 2 km south, and then runs on a path that takes him directly back to the place he started at. a. How far did John run? b. If he has run at an average speed of 4 m/s, how long did the entire run take? (Answers: a. 6.83 km; b. 28.5 min) 9. John and Al are in a 15 km race. John averages 4.4 m/s during the first half of the race and then runs at a speed of 4.2 m/s until the last 200 m, which he covers at 4.5 m/s. At what average speed must Al run to beat John? (Answer: > 4.3 m/s) 10. A sailboat heads north at 3 m/s for 1 hour and then tacks back to the southeast (at 45° to north) at 2 m/s for 45 minutes. a. How far has the boat sailed? b. How far is it from its starting location? (Answers: a. 16.2 km; b. 8.0 km) William Perry, defensive tackle and part-time running back better known as “The Refrigerator,” weighed in at 1352 N during his 1985 rookie season with the Chicago Bears. What was Perry’s mass? (Answer: 138 kg) 2. How much force must be applied to a 0.5-kg hockey puck to give it an acceleration of 30 m/s 2 ? (Answer: 15 N) 3. A rugby player is contacted simultaneously by three opponents who exert forces of the magnitudes and directions shown in the diagram at

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right. Using a graphic solution, show the magnitude and direction of the resultant force. 6. A gymnastics floor mat weighing 220 N has dimensions of 3 m × 4 m × 0.04 m. How much pressure is exerted by the mat against the floor? (Answer: 18.33 Pa) 7. What is the volume of a milk crate with sides of 25 cm, 40 cm, and 30 cm? (Answer: 30,000 cm 3 or 30 l) 9. If the contents of the crate described in Problem 7 weigh 120 N, what are the average density and specific weight of the box and contents? (Answer: 0.0004 kg/cm 3 ; 0.004 N/cm 3 ) 10. Two children sit on opposite sides of a playground seesaw. Joey, who weighs 220 N, sits 1.5 m from the axis of the seesaw, and Suzy, who weighs 200 N, sits 1.7 m from the axis of the seesaw. How much torque is created at the axis by each child? In which direction will the seesaw tip? (Answer: Joey, 330 N-m; Suzy, 340 N-m; Suzy’s end) ADDITIONAL PROBLEMS 1. What is your own body mass in kg? 2. Gravitational force on planet X is 40% of that found on the earth. If a person weighs 667.5 N on the earth, what is the person’s weight on planet X? What is the person’s mass on the earth and on planet X? (Answer: weight on planet X = 267 N; mass = 68 kg on either planet) 3. A football player is contacted by two tacklers simultaneously. Tackler A exerts a force of 400 N, and tackler B exerts a force of 375 N. If the

forces are coplanar and directed perpendicular to each other, what is the magnitude and direction of the resultant force acting on the player? (Answer: 548 N at an angle of 43° to the line of action of tackler A) 4. A 75-kg skydiver in free fall is subjected to a crosswind exerting a force of 60 N and to a vertical air resistance force of 100 N. Describe the resultant force acting on the skydiver. (Answer: 638.6 N at an angle of 5.4° to vertical) 5. Use a trigonometric solution to find the magnitude of the resultant of the following coplanar forces: 60 N at 90°, 80 N at 120°, and 100 N at 270°. (Answer: 49.57 N) 6. If 37% of body weight is distributed above the superior surface of the L5 inter-vertebral disc and the area of the superior surface of the disc is 25 cm 2 , how much pressure exerted on the disc is attributable to body weight for a 930 N man? (Answer: 13.8 N/cm 2 ) 7. In the nucleus pulposus of an intervertebral disc, the compressive load is 1.5 times the externally applied load. In the annulus fibrosus, the compressive force is 0.5 times the external load. What are the compressive loads on the nucleus pulposus and annulus fibrosus of the L5-S1 intervertebral disc of a 930-N man holding a 445-N weight bar across his shoulders, given that 37% of body weight is distributed above the disc? (Answer: 1183.7 N acts on the nucleus pulposus; 394.5 N acts on the annulus fibrosus.)

8. Estimate the volume of your own body. Construct a table that shows the approximate body dimensions you used in formulating your estimate. 9. Given the mass or weight and the volume of each of the following objects, rank them in the order of their densities. 77 OBJECT WEIGHT OR MASS VOLUME A 50 kg 15.00 in 3 B 90 lb 12.00 cm 3 C 3 slugs 1.50 ft 3 D 450 N 0.14 m 3 E 45 kg 30.00 cm 3 10. Two muscles develop tension simultaneously on opposite sides of a joint. Muscle A, attaching 3 cm from the axis of rotation at the joint, exerts 250 N of force. Muscle B, attaching 2.5 cm from the joint axis, exerts 260 N of force. How much torque is created at the joint by each muscle? What is the net torque created at the joint? In which direction will motion at the joint occur? (Answer: A, 7.5 N-m; B, 6.5 N-m; net torque equals 1 N-m in the direction of A) A runner completes 6½ laps around a 400 m track during a 12 min (720 s) run test. Calculate the following quantities: a. The distance the runner covered b. The runner’s displacement at the end of 12 min c. The runner’s average speed d. The runner’s average velocity

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e. The runner’s average pace (Answers: a. 2.6 km; b. 160 m; c. 3.6 m/s; d. 0.22 m/s; e. 4.6 min/km) 2. A ball rolls with an acceleration of −0.5 m/s 2 . If it stops after 7 s, what was its initial speed? (Answer: 3.5 m/s) 3. A wheelchair marathoner has a speed of 5 m/s after rolling down a small hill in 1.5 s. If the wheelchair underwent a constant acceleration of 3 m/s 2 during the descent, what was the marathoner’s speed at the top of the hill? (Answer: 0.5 m/s) 4. An orienteer runs 400 m directly east and then 500 m to the northeast (at a 45° angle from due east and from due north). Provide a graphic solution to show final displacement with respect to the starting position. 5. An orienteer runs north at 5 m/s for 120 s and then west at 4 m/s for 180 s. Provide a graphic solution to show the orienteer’s resultant displacement. 6. Why are the horizontal and vertical components of projectile motion analyzed separately? 7. A soccer ball is kicked with an initial horizontal speed of 5 m/s and an initial vertical speed of 3 m/s. Assuming that projection and landing heights are the same and neglecting air resistance, identify the following quantities: a. The ball’s horizontal speed 0.5 s into its flight b. The ball’s horizontal speed midway through its flight c. The ball’s horizontal speed immediately before contact with the ground d. The ball’s vertical speed at the apex of the flight e. The ball’s vertical speed midway through its flight f. The ball’s vertical speed immediately before contact with the

ground 8. If a baseball, a basketball, and a 71.2-N shot were dropped simultaneously from the top of the Empire State Building (and air resistance was not a factor), which would hit the ground first? Why? 9. A tennis ball leaves a racket during the execution of a perfectly horizontal ground stroke with a speed of 22 m/s. If the ball is in the air for 0.7 s, what horizontal distance does it travel? (Answer: 15.4 m) 10. A trampolinist springs vertically upward with an initial speed of 9.2 m/s. How high above the trampoline will the trampolinist go? (Answer: 4.31 m) 4. A buoy marking the turn in the ocean swim leg of a triathlon becomes unanchored. If the current carries the buoy southward at 0.5 m/s, and the wind blows the buoy westward at 0.7 m/s, what is the resultant displacement of the buoy after 5 min? (Answer: 258m; 􀄟 = 54.5° west of due south) 5. A sailboat is being propelled westerly by the wind at a speed of 4 m/s. If the current is flowing at 2 m/s to the northeast, where will the boat be in 10 min with respect to its starting position? (Answer: D = 1.8 km; 􀄟 = 29° north of due west) 6. A Dallas Cowboy carrying the ball straight down the near sideline with a velocity of 8 m/s crosses the 50-yard line at the same time that the last Buffalo Bill who can possibly hope to catch him starts running from the 50-yard line at a point that is 13.7 m from the near sideline. What must the Bill’s velocity be if he is to catch the Cowboy just short

of the goal line? (Answer: 8.35 m/s) 7. A soccer ball is kicked from the playing field at a 45° angle. If the ball is in the air for 3 s, what is the maximum height achieved? (Answer: 11.0 m) 8. A ball is kicked a horizontal distance of 45.8 m. If it reaches a maximum height of 24.2 m with a flight time of 4.4 s, was the ball kicked at a projection angle less than, greater than, or equal to 45°? Provide a rationale for your answer based on the appropriate calculations. (Answer: >45°) 9. A badminton shuttlecock is struck by a racket at a 35° angle, giving it an initial speed of 10 m/s. How high will it go? How far will it travel horizontally before being contacted by the opponent’s racket at the same height from which it was projected? (Answer: d v = 1.68 m; d h = 9.58 m) 10. An archery arrow is shot with a speed of 45 m/s at an angle of 10°. How far horizontally can the arrow travel before hitting a target at the same height from which it was released? (Answer: 70.6 m) The relative angle at the knee changes from 0° to 85° during the knee flexion phase of a squat exercise. If 10 complete squats are performed, what is the total angular distance and the total angular displacement undergone at the knee? (Provide answers in both degrees and radians.) (Answer: ϕ = 1700°, 29.7 rad; θ = 0)

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2. Identify the angular displacement, the angular velocity, and the angular acceleration of the second hand on a clock over the time interval in which it moves from the number 12 to the number 6. Provide answers in both degree- and radian-based units. (Answer: θ = −180°, −π rad; ω = −6 deg/s, −π/30 rad/s; α = 0) 3. How many revolutions are completed by a top spinning with a constant angular velocity of 3 π rad/s during a 20 s time interval? (Answer: 30 rev) 4. A kicker’s extended leg is swung for 0.4 s in a counterclockwise direction while accelerating at 200 deg/s 2 . What is the angular velocity of the leg at the instant of contact with the ball? (Answer: 80 deg/s, 1.4 rad/s) 5. The angular velocity of a runner’s thigh changes from 3 rad/s to 2.7 rad/s during a 0.5 s time period. What has been the average angular acceleration of the thigh? (Answer: −0.6 rad/s 2 , −34.4 deg/s 2 ) 10. A tennis racquet swung with an angular velocity of 12 rad/s strikes a motionless ball at a distance of 0.5 m from the axis of rotation. What is the linear velocity of the racquet at the point of contact with the ball? (Answer: 6 m/s) ADDITIONAL PROBLEMS 1. A 1.2-m golf club is swung in a planar motion by a right-handed golfer with an arm length of 0.76 m. If the initial velocity of the golf ball is

35 m/s, what was the angular velocity of the left shoulder at the point of ball contact? (Assume that the left arm and the club form a straight line, and that the initial velocity of the ball is the same as the linear velocity of the club head at impact.) (Answer: 17.86 rad/s) 2. David is fighting Goliath. If David’s 0.75-m sling is accelerated for 1.5 s at 20 rad/s 2 , what will be the initial velocity of the projected stone? (Answer: 22.5 m/s) 3. A baseball is struck by a bat 46 cm from the axis of rotation when the angular velocity of the bat is 70 rad/s. If the ball is hit at a height of 1.2 m at a 45° angle, will the ball clear a 1.2-m fence 110 m away? (Assume that the initial linear velocity of the ball is the same as the linear velocity of the bat at the point at which it is struck.) (Answer: No, the ball will fall through a height of 1.2 m at a distance of 105.7 m.) 4. A polo player’s arm and stick form a 2.5-m rigid segment. If the arm and stick are swung with an angular speed of 1.0 rad/s as the player’s horse gallops at 5 m/s, what is the resultant velocity of a motionless ball that is struck head-on? (Assume that ball velocity is the same as the linear velocity of the end of the stick.) (Answer: 7.5 m/s) 5. Explain how the velocity of the ball in Problem 4 would differ if the stick were swung at a 30° angle to the direction of motion of the horse. 6. List three movements for which a relative angle at a particular joint is

important and three movements for which the absolute angle of a body segment is important. Explain your choices. 7. A majorette in the Rose Bowl Parade tosses a baton into the air with an initial angular velocity of 2.5 rev/s. If the baton undergoes a constant acceleration while airborne of −0.2 rev/s 2 and its angular velocity is 0.8 rev/s when the majorette catches it, how many revolutions does it make in the air? (Answer: 14 rev) 8. A cyclist enters a curve of 30-m radius at a speed of 12 m/s. As the brakes are applied, speed is decreased at a constant rate of 0.5 m/s 2 . What are the magnitudes of the cyclist’s radial and tangential accelerations when his speed is 10 m/s? (Answer: a r = 3.33 m/s 2 ; a t = −0.5 m/s 2 ) 9. A hammer is being accelerated at 15 rad/s 2 . Given a radius of rotation of 1.7 m, what are the magnitudes of the radial and tangential components of acceleration when tangential hammer speed is 25 m/s? (Answer: a r = 367.6 m/s 2 ; a t = 25.5 m/s 2 ) 10. A speed skater increases her speed from 10 m/s to 12.5 m/s over a period of 3 s while coming out of a curve of 20-m radius. What are the magnitudes of her radial, tangential, and total accelerations as she leaves the curve? (Remember that a r and a t are the vector components of total acceleration.) (Answer: a r = 7.81 m/s 2 ; a t = 0.83 m/s 2 ; a = 7.85 m/s 2 )

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