In this exercise, the first of a series, we will makeconnections between the physics you have been learning (in thiscase, kinematics) and how it is used by people in their work andresearch. Today we consider an example from kinesiology research,based on a 2000 paper from the Journal of Measurement in PhysicalEducation and Exercise Science (nota bene: you do not have to readthis paper, or any of the hyperlinks to follow the exercise – it isonly provided here for your interest).
Jumping is an activity common to many sports, such asbasketball, volleyball, and others. An important part of trainingto improve jumping ability is tracking your progress: how else willyou decide if your chosen routine is working? Researchers in thefield , as well as professional athletes and their coaches , use avariety of techniques to accurately measure the vertical jumpheight. One approach is straightforward: just \"see\" how high youjump! To do it accurately, however, you need high speed cameras, away of calculating the position of the body's centre of mass,balancing torques... very complicated. Or you can use the old\"reach\" method, having subjects jump and touch the highest pointthey can reach with a chalk-covered palm – but now you have tocorrect for differential arm length, swing timing... rathercrude.
However, with your knowledge of kinematics, you can get awaywith as little as a stopwatch, saving valuable time and money.Below we will get you to follow in the footsteps of pioneeringkinesiologists and exercise scientists and re-invent two of thesephysics-based methods. (By the way, this kind of use of mechanicsin biology is called biomechanics.)
a) (Please refrain from looking at the rest of the questionuntil you have given this part some thought: not to worry, no wronganswers here!) Given your knowledge of kinematics, what variablewould you want to measure to be able to calculate someone'svertical jump height? Please explain in a few words how you wouldgo about doing this.
b) Suppose you could measure the time of flight ?flight. Howwould you calculate the vertical jump height â„Ž? (Unsurprisingly,this is called the time-of-flight method . Calculate the predictedheight for the following times-of-flight: 0.827 s (LeBron James),0.846 s (Michael Jordan), 0.864 s (Wilt Chamberlain), 0.53 s (theauthor of this exercise).
c) What about if you measured the vertical take-off velocity?=(0,??) instead? (This is known as the impulse-momentum method ,because of the way the take-off velocity is calculated using aforce platform). Calculate the predicted height for the followingtake-off velocities: 3.91 m/s (LeBron James), 4.00 m/s (MichaelJordan), 4.09 m/s (Wilt Chamberlain), 2.60 m/s (the author of thisexercise).
d) Suppose you have both numbers: would you expect them to beconsistent, i.e., to give the same predicted vertical jump height?Give your reasons. How might you check for consistency?
e) Use the two datasets from the previous parts of this problemto check consistency. Were you right? If you found aninconsistency, list some of the reasons behind this inconsistency.If not, explain why you should expect them to be consistent.
