Free Throw shooting is an
important aspect of the game; it is essential that all athletes no matter their
position are successful from the Free Throw line. With Coaching, most athletes
will approach the free throw line by first aligning their feet. If right
handed, the right foot would align with the split line, slightly in front of
the left foot, shoulder width apart. This will ensure that the athlete is stable
and balanced when shooting the ball. The reason that the right foot aligns with
the spilt line is so that the ball should only miss long or short therefore
making it more accurate and there is less to adjust in your shot after you
miss. Each athlete is different but most takes one or two dribbles of the
basketball and then brings the ball up onto their fingers where the index
finger aligns with a groove on the ball, and then the athlete will shoot the
ball. Holding their follow through by locking their elbow and snapping their
wrist. This YouTube clip gives a good and accurate explanation of how to shoot
a Free Throw.
Source: This picture was taken from http://www.lunch.com/reviews/sports_league/UserReviewNBA1453236158114Underhanded_Free_Throws_Time_For_a_Comeback_.html This picture illustrates the teaching cues of a Free Throw. 
The Answer:
Newton’s Laws:
First Law: 'An object will remain at rest or continue to move with constant velocity as
long as the net force equals zero' (Blazevich, 2010, p.44). The tendency of an object to remain in its
present state is called Inertia. All objects with a mass have inertia, the
larger the mass the more inertia to overcome therefore making it more difficult
to speed up, slows down or change direction (Blazevich, 2010, p. 44). When
shooting a Free Throw the athlete needs to change their state from rest to a
vertical motion.
Second Law: ‘The
acceleration of an object is proportional to the net force acting on it and
inversely proportional to the mass of the object F=M x A’ (Blazevich, 2010, p.
45) in order to change a state of motion it is required to apply force. The
equation F= M×A tells us that to accelerate an object faster we must apply more
force (Blazevich, 2010, p. 45). To shoot a Free Throw, the athlete must apply
force in order to accelerate the ball.
Third Law: ‘For
every action, there is an equal and opposite reaction’ (Blazevich,
2010, p. 45). When we walk, run or jump we apply force
against earth, the earth applies an equal and opposite force in order to move
us. This is evident in the Free Throw when a vertical or downward force is
applied when the foot contacts the ground, the ground exerts an equal and
opposite reaction force. These forces can accelerate the athlete forward or
vertical if the force is great enough to overcome inertia.
Source: Blazevich, 2010, p.45. This diagram demonstrates how we must apply a downward force in order for an equal and opposite reaction to propel us into the air vertically. 
The Law of
Gravitation: ‘All bodies are attracted to each other with a force proportional
to the product of the two masses and inversely proportional to the square of
the distance between them’ (Blazevich, 2010, p. 46).
Gravity will
have less influence if the product of two masses is smaller; therefore Gravitational
force is less when we are lighter. The net force causing acceleration in the
upward direction is equal to the upward directional force plus the downwards
gravitational force (this is a negative factor as it acts downwards). Inertia
is relative to the mass of the object, so heavier objects require a larger
force to accelerate, this is enlarged when an object is moving vertically because
of the gravitational force. Which is evident in a Free Throw as the athlete is
moving vertically, bending their legs and applying force into the ground, to
come up on to their toes or to jump slightly. So, because of gravitational
force we much use a larger force.
All three of
Newton’s Laws and the Law of Gravitation work together to allow the athlete to
come up onto their toes or jump slightly to shoot the Free Throw. The athlete
needs to overcome inertia by having a applied force against them, to do this
they must apply a large and welldirected force against the earth which applies
an equal and opposite reaction force against them, which also the shooter to
come up into their toes or jump slightly. Because of Newton’s law of
gravitation it is necessary to produce large vertical forces, or have a low
body mass in order to jump higher.
Source: (Taken by H. Richards) This picture shows how the athlete bends their knees in order to apply force to accelerate the object. 
Projectile Motion:
This is the
motion of an object projected at an angle into the air. Factors that can
influence an objects trajectory include gravity and air resistance. A projection can move at any angle between 0
degrees (horizontal) or 90 degrees (vertical). Trajectory is influenced by the
projection speed, the projection angle and the relative height of projection (Blazevich,
2010, p. 25).
Projection
speed: the distance and projectile covers is determined by its projection
speed, the faster the speed the further it will go. In the free throw the
projectile or the basketball moves vertically, therefore the projection speed
will determine the height is reaches before gravity accelerates it back to
earth.
Projectile
angle: This affects the range of a projectile. When an object is projected at
angles between 0 degrees and 90 degrees, the object will travel vertically and
horizontally. When the angle is greater the object attains greater vertical
height but less range.
Relative
height of projection: This is the vertical distance between the projection
point of an object and the point in which it lands.
This greater
angle is good for a Free Throw the optimum angle for a Free Throw is
approximately 51 degrees (Gordon, 1997, p. 495). As this needs a greater angle of projection to
improve the accuracy of the shot, the ball is more likely to go in if it falls
vertically then when it skims across the top of the basket. In the end it would
be necessary to run biomechanical tests to determine the optimum trajectory for
the basketball, based on the individual athlete who is shooting it because of
physiological features such as height or arm length can alter the optimum angle.
Source: Photo taken from http://en.zero.wikipedia.org/wiki/Lauren_Jackson: This demonstrates how the athlete releases the ball from a large angle to allow the ball to fall vertically into the ring. 
The Magnus Effect:
This YouTube clip gives a good
general understanding of the Magnus effect:
By
understanding the importance of Spin, performance of the Free Throw can be
improved. By Appling more backspin on
the basketball if you shot long or short you have a higher change of the ball
going in if it has backspin because it is more likely to bounce up and drop
into the basket (Hubbard, 206, pp. 13031308). Soft hands on the ball is
crucial, this is done by the athlete having the ball on their fingers and no part
of the ball touching on the palm of their hands. By the action of snapping the
wrist it allows the ball to come off the fingers with backspin.
Momentum:
We need
force to get an object to exert velocity in order to overcome inertia. If the
force is exerted in the correct direction we will be accelerated in the desired
direction. In order to change an objects momentum we need to apply force. To
accelerate vertically we need larger vertical impulses, this will propel us
into the air. Impulse is a production of force and time therefore the greater
the impulse the greater the change in momentum (Blazevich, 2010, pp.
5254). This biomechanical principle is
present in a foul shot when the athlete is bending their legs pushes force as a
vertical impulse into the ground in order to propel themselves up onto their
toes or in to propel themselves into the air slightly.
Summation of Forces:
The sum of
forces is the momentum given to the object in this case the ball generated by
each body part. To generate maximum momentum using each segment of the body
from the large muscles in the legs into the small muscles last to generate
force. Correct timing, through to the
great range of motion will gain maximum momentum (Brancazio, 1981, p. 358). To attain power, efficacy and accuracy in the
shot the whole body is used. The shot begins with the movement of the legs,
pushing into the ground. The force then travels from the legs into the
shoulders, into the forearms and into the tips of the fingers when the ball is
released.
Source: Picture Taken from http://offthebackboard.wordpress.com/2011/07/17/thelistbestfreethrowroutines/ This picture illustrates how the muscles work together in summation to generate force. 
Kinetic Chain:

Work, Energy and Power
‘The amount
of work done is equal to the average force that is applied multiplied by the
distance of which it is applied. W= F x D’ (Blazevich, 2010, p. 100).
This is a product
of force and displacement, force provided over a range of object movement.
Power is the
‘rate of doing work, work per unit time or the product of force and velocity’ (Blazevich,
2010, pp. 101102).
Kinetic
energy is associated with velocity of our body or a motion of a body with
greater mass (Blazevich, 2010, p. 103).
Kinetic energy is present in a Free Throw as there is movement of the athlete’s
body.
By
understanding the relationship between work, power and energy we can improve
performance of a Free Throw. All these components of power, work and energy are
present when the athlete is bending up and onto their toes in order to push the
ball up towards the basket; it is present throughout the whole action of the
Free Throw.
How else we can use this information:
The Netball
shot and a set shot in basketball are very closely related to the biomechanical
principles of a Free Throw. In an Netball shot athletes with align their feet
with the basket and then bend their knees, pushing into the ground in order to
propel their feet into the air, just like a Free Throw the only difference
between these two shots is the follow through where basketball athletes lock
and snap their wrist of the shooting hand and netballers follow through with
two hands. A set shot in basketball is where an athlete is open for a shot with
no defenders on them (just like a Foul Shot), so all that is required for the
athlete is to catch and shoot. The only difference in the two shots is the
force required for the athlete to propel himself or herself into the air higher.
The
biomechanical principles like newton’s second law, vertical impulse, work,
power and the kinetic chain can all be altered in order to maximise other
aspects of the sport of basketball such as the component of rebounding where
the principle can be used to maximise jump height and energy required for
repeated jumps. This may also relate to volleyball where blockers have to not only
jump high but also lower their energy cost for repeated jumps. Another
component of basketball where some principles relate are the dunk where
athletes need to jump high and stretch up with a angle to get the ball over the
ring.
References:
Blazevich, A. (2010). Sports biomechanics, the basics: Optimising human performance. A&C Black.
Brancazio,
P. J. (1981). Physics of basketball. American Journal of Physics, 49, 356365.
Gordon
R, Hamilton & Christoph, Reinschmidt. (1997). Optimal Trajectory for the
basketball free throw. Journal of Sports Sciences, 15(5), 491504.
Hubbard,
H & Okubo, M. (2006). Dynamics of the basketball shot with application to the
free throw. Journal of sports science, 24(12), 1303.