This document discusses the use of math in several sports. It begins by explaining the movement of a ball over a plane surface and impact times. It then provides examples of how math applies to basketball, baseball, and soccer. For basketball, it discusses variables like the court dimensions, basket height, and three point line distance. For baseball, it mentions the "sweet spot" of hitting and how a curve ball curves through the air. And for soccer, it notes that it is a game of angles between goaltending and shooting.

2. Submitted By
Name : Nirnay Mukharjee
ID : 143-15-4421
Section : M
Department of CSE
Faculty of FSIT

3. Issues To Be Discussed
1. The movement of a ball over a plane surface
2. Impact Times
2. Real World Application
- Basketball
- Baseball
- Soccer

4. The Movement of a Ball over a
plane Surface
Central blow over a horizontal surface
Consider a ball of mass M and radius a.
Let coefficient of Sliding friction be µ
Then friction on Ball – F= µMg (1)
This force will have 2 consequences
(i) Linear deceleration of ball
(ii) moment of force about C (centre) will produce a
clockwise angular acceleration

5. Continued
 Application to billiard balls
 The sliding coefficient of an average
billiard table is about 0.2, velocity
of a strongly cued ball ≈ 3ms
therefore duration of sliding phase
is = t = 2(3)/(49)(0.2)(9.8) = 0.4 secs
 Using (13) distance travelled = 1.1m

6. Impact Times
 In most games, experiments indicate that the linear
compression x of a golf ball is related to the applied
force F by a law of the form of F=Kx
 This leads to a relation between impact times and
velocity, As velocity increases, the duration of impact
decrease, approaching a constant value at higher
velocities

7. Continued
Forces at impact
in a golf drive, velocity of ball of tee ≈70ms , time of
impact = 0.0005secs, mass of ball = 0.046kg.
By Newton (ii) (average force)
= 0.046 * 70 / 0.0005 = 6300N
This is the average force at impact since it must be zero
at the start and finish of impact, it is reasonable to
suppose that MAX force occurs at midway throughout
the impact 6300 * 2 = 12600N

8. Math in Basketball
 Score Keeping
 2 point, 3 point shots
 Free throws
 94’ by 50’ court
 Basket 10’ off the ground
 Ball diameter 9.5”
 Rim diameter 18.5”
 3 point line about 24’ from
basket
 Think of any ways math can
be used in basketball?

9. Continued
 Basketball Shot
 At what velocity should a foul shot be taken?
 Assumptions/Given:
 Distance
 About 14 feet (x direction) from FT line to
middle of the basket
 Height
 10 feet from ground to rim
 Angle of approach
 Close to 90 degrees as possible
 Most are shot at 45 degrees
 Ignoring air resistance

10. Math in Baseball
 Sweet Spot” of hitting a baseball
-When bat hits ball, bat vibrates
– Frequency and intensity depend on location of contact
– Vibration is really energy being transferred from ball to
the bat (useless)

11. Continued
 Pitching a Curve Ball
 Ball thrown with a downward
spin. Drops as it approaches
plate
 For years, debated whether
curve balls actually curved
or it was an optical illusion
 With today’s technology,
it’s easy to see that they
do indeed curve

12. Math in Soccer
 Soccer is a game of angles”
 Goaltending vs
Shooting

13. Angles in Soccer
 May think it best to stand in a position that bisects
goal line
 Gives shooter more room between goalie and left post,
than right post

14. Thank You