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Calculus in Basketball
Transcript of Calculus in Basketball
Let's imagine that a standard basketball
court is viewed as a typical X, Y grid.
The shooting guard, J.J. Redick,
stands at 6'4" at the origin of the
basketball court. The basketball hoop is
located at distance, d, away from the shooter.
The hoop stands at a standard height
of 10 feet(3.05 m); putting the the hoop at point (d, 10).
The release point of the ball is at a height
of 7 feet(2.13 m),due to the fact that the
shooter releases the ball over his head.
The point at which the ball is located is at (0, 7).
Arc Length of a Shot
Equations to understand:
Horizontal direction: x(t)=xº+vºcos(ø)t
Vertical direction: y(t)=yº+vºsin(ø)t+(1/2)gt^2
xº=initial horizontal position
yº=initial vertical position
g= acceleration with respect to gravity
Arc length equation:
Deriving the Equation
After substituting the current position
of the ball, (0,7), or (0,2,13):
x(t)= v° cos(ø)t
y(t)= 2.13+ v° sin(ø)t-4.905t²
The Derivatives of x(t) and y(t) with respect to time (t) are:
dx/dt= v° cos (ø)
dy/dt= v° sin (ø) - 9.81t
L= sqrt(v° cos(ø))² +(v° sin (ø)- 9.81t)² =
sqrtv° ² cos² (ø) + v° ² sin² (ø) - 19.62 * t * v° sin(ø) = 96.24t² dt
sqrtv° ² -19.62 * t * v° sin (ø) + 96.24t² dt
L= sqrt2.24² - 19.62 * 2 * (2.24 sin(45) + 96.24 (2)² dt
L= 17.34 m/s
Probability of making 5 3-pointers in a row
Redick's 3 point field goal percentage in the 2013-14 NBA season: 39.5%
Ben Levi, Period 2
Calculus in a Basketball Shot
3 point shot #1
3 point shot #2
3 point shot #3
3 point shot #4
3 point shot #5
39.5% x 39.5 % x 39.5% x 39.5% x 39.5% = X
39.5%^5 ---> 0.395^5= 0.0096
Probability of making 5 3-pointes in a row: 0.96%
ESPN. ESPN Internet Ventures, n.d. Web. 12 Nov. 2014. <http://espn.go.com/nba/statistics/player/_/stat/3-points/sort/threePointFieldGoalPct/year/2014>.
basketball, along with other
sports, can be analyzed
through the use of
science and mathematics.
Highnessfsk. "Sport Science: Stephen Curry." YouTube. YouTube, 15 May 2013. Web. 18 Nov. 2014.