| Title | Modeliranje slobodnih bacanja |
| Author | Nikolina Mihić |
| Mentor(s) | Ivan Matić (thesis advisor)
|
| Abstract | U ovom radu smo izveli model slobodnih bacanja kako bi zaključili što je sve potrebno
za uspješno slobodno bacanje. Započeli smo sa pojednostavljenim modelom
s određenim pretpostavkama te smo pretpostavili da su nam za model najbitniji
visina igrača i početni kut. Ne možemo očekivati da će igrač pri svakom izvođenju
slobodnog bacanja moći držati početnu brzinu konstantnom pa se ovaj model nije
pokazao najboljim. Vidjeli smo da postoje razlike u početnoj brzini i kutu kod
igrača različitih visina te da niži igrači trebaju ispucati loptu pod većim kutem.
U drugom modelu smo dopustili da u isto vrijeme i neovisno variraju početna
brzina i kut. Tražili smo idealnu putanju lopte sa najvećim mogućim odstupanjima
u početnom kutu i brzini, ali pod uvjetom da lopta i dalje ulazi u koš. Izbacili smo
pretpostavku da lopta mora proći kroz centar obruča. Prvi zaključak do kojeg smo
došli je da će najbolja putanja prvenstveno ovisiti o individualcu i načinu na koji
on šutira. Iz slika smo vidjeli da najbolja putanja nije ona koji prolazi kroz centar
obruča te da je putanja koja dozvoljava maksimalu pogrešku ona koja prolazi između
centra obruča i drugog obruča. Također smo vidjeli da nam je bitnija konzistentnost
u brzini, nego u kutu, tj. da je putanja osjetljivija na promjene u brzini, nego u
kutu. Veće greške možemo raditi pri većim brzinama. Igrači koji imaju problem
s kontroliranjem brzine, trebali bi loptu ispuštati pod većim kutem u odnosu na
prosjek. Ako imamo više problema sa kontroliranjem brzine, onda ćemo na brzinu
staviti veću težinu kako bi dobili više prostora za pogreške.
Vidjeli smo da na model mogu utjecati i otpor zraka, tvrdoća obruča, koeficijent,
odskakivanje ili rotacija lopte. Model možemo promatrati i u trodimenzionalnom
sustavu, koji dobijemo ukoliko izbacimo pretpostavku da lopta neće skrenuti sa putanje. |
| Keywords | basketball mathematical modeling initial angel initial velocity trajectory |
| Parallel title (English) | Modeling Basketball Free Throws |
| Committee Members | Domagoj Ševerdija (committee chairperson)
Ivan Matić (committee member)
Slobodan Jelić (committee member)
|
| Granter | Josip Juraj Strossmayer University of Osijek
Department of Mathematics |
| Lower level organizational units | Chair of Pure Mathematics
Algebra and Calculus Research Group |
| Place | Osijek |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics |
| Study specialization | Financial and Statistical Mathematics |
| Academic title abbreviation | mag.math. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2017-06-20 |
| Parallel abstract (English) | In this paper, we conducted a free throw model to find out what is needed
for a successful free throwing. We started with a simplified model with certain
assumptions and we assumed that player’s height and the initial angle are the most
important for the model. We can not expect from player to keep the initial velocity
constant at each free throw he perform, so this model is not quite the best. We have
seen that there are differences in initial angel and velocity for players of different
altitudes, so the lower player should shot the ball at greater angle.
In the second model we allowed variation of initial speed and angle at the same
time and independently. We were looking for an ideal velocity for the ball with the
maximum possible deviations in the initial angel and velocity, but providing that
ball still enters the basket. Furthermore, we have excluded the assumption that the
ball must pass through the center of the hoop. The first conclusion we come across
is that the best trajectories will primarily depend on the individual and the manner
in which he or she shots the ball. From the pictures we saw that the best trajectory
is not the one that passes through the center of the hoop and that the trajectory
that permits the maximum mistake is the one that passes between the center of the
hoop and the second hoop. Also, we noticed that consistency in velocity is more
important than one in the angle, that is, the trajectory is more sensitive to velocity
changes rather than the angle’s. Bigger mistakes we can still make at high velocity.
Players who have problems with velocity control should drop the ball at a greater
angle than the average. If we have problems controlling the velocity, then we should
put weight on the velocity in order to get more space for the mistakes.
To conclude, we have seen that the model can also be affected by air resistance,
coefficient of restitution of the ball, softness of the rim, bounce or rotation of the
ball. We can also observe the model in a three-dimensional system which we get
removing the assumption that the ball will not turn from the path. |
| Parallel keywords (Croatian) | košarka matematičko modeliranje početni kut početna brzina putanja |
| Resource type | text |
| Access condition | Open access |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:126:967811 |
