Question

In this exercise, the first of a series, we will make connections between the physics you have been learning (in this case, kinematics) and how it is used by people in their work and research. Today we consider an example from kinesiology research, based on a 2000 paper from the Journal of Measurement in Physical Education and Exercise Science (nota bene: you do not have to read this paper, or any of the hyperlinks to follow the exercise – it is only provided here for your interest).

Jumping is an activity common to many sports, such as basketball, volleyball, and others. An important part of training to improve jumping ability is tracking your progress: how else will you decide if your chosen routine is working? Researchers in the field , as well as professional athletes and their coaches , use a variety of techniques to accurately measure the vertical jump height. One approach is straightforward: just "see" how high you jump! To do it accurately, however, you need high speed cameras, a way 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 point they can reach with a chalk-covered palm – but now you have to correct for differential arm length, swing timing... rather crude.

However, with your knowledge of kinematics, you can get away with as little as a stopwatch, saving valuable time and money. Below we will get you to follow in the footsteps of pioneering kinesiologists and exercise scientists and re-invent two of these physics-based methods. (By the way, this kind of use of mechanics in biology is called biomechanics.)

a) (Please refrain from looking at the rest of the question until you have given this part some thought: not to worry, no wrong answers here!) Given your knowledge of kinematics, what variable would you want to measure to be able to calculate someone's vertical jump height? Please explain in a few words how you would go about doing this.

b) Suppose you could measure the time of flight ?flight. How would you calculate the vertical jump height ℎ? (Unsurprisingly, this is called the time-of-flight method . Calculate the predicted height for the following times-of-flight: 0.827 s (LeBron James), 0.846 s (Michael Jordan), 0.864 s (Wilt Chamberlain), 0.53 s (the author 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 a force platform). Calculate the predicted height for the following take-off velocities: 3.91 m/s (LeBron James), 4.00 m/s (Michael Jordan), 4.09 m/s (Wilt Chamberlain), 2.60 m/s (the author of this exercise).

d) Suppose you have both numbers: would you expect them to be consistent, 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 problem to check consistency. Were you right? If you found an inconsistency, list some of the reasons behind this inconsistency. If not, explain why you should expect them to be consistent.

Answer 1