Projectile motion

Projectile motion is a term that describes the path an object takes through the air when it travels through the air at an angle (Blazevich, 2013). Objects such as a basketball are released into the air at an angle and as such have vertical and horizontal velocity. External forces that affect the basketball when travelling through the air are gravity and air resistance, where gravity is a constant force of 9.81 m/s² (Blazevich, 2013). The trajectory of a basketball when launched into the air is influenced by projection speed, projection angle and the relative height of projection, all of which can be controlled by the player shooting the basketball.

The easiest way for a basketball player to change the trajectory of the basketball is to add more force to the ball, giving it a greater projection speed. The greater the horizontal and vertical projection speed the more flight time the basketball will have and the further it will travel. The horizontal trajectory speed can be calculated easily by dividing the distance travelled by the time taken to complete the trajectory as the horizontal speed will remain constant unless acted upon by external forces. In the case of a basketball the air resistance will slow the horizontal velocity, but only slightly. Similarly the vertical velocity can be configured if we take into account the effect of gravity on the ball. A useful equation for calculating vertical velocity is Vf = Vi + at, where Vf is final velocity, Vi is initial velocity, a is acceleration and t equals time (Blazevich, 2013). If we consider a basketball jump shot from the three point line it takes about one second from release to reach its highest point.

 Therefore t=1 a= 9.8 and Vf= 0.

0 = Vi + 9.8

Vi = 9.8 m/s

While projection speed is important for achieving desired range when shooting a basketball the projection angle will affect the range as well as the chance of the ball falling through the basket cleanly. A basketball can be projected at angles between 0 and 90 degrees where a release point of 90 degrees will result in the ball travelling solely vertically up and downwards without covering any horizontal distance. The optimal release point for maximum range of any projectile is 45 degrees as this will give the projectile equal components of horizontal and vertical velocities (Blazevich, 2013). According to research the optimal release angle for a basketball jump shot is 52 degrees (Knudson, 1993). This is due to the fact that the ball must enter the basket vertically and this added vertical height gives a bigger target basket for the ball to fall through as we can see in the diagram below.

                                                    (Okazaki & Rodacki, 2012)

Another factor affecting the basketballs trajectory is the relative height of projection. In a jump shot the height of projection is affected by the player’s height, the distance of their arm extension and the height of their jump. Defending players will also effect the height of projection so release points will vary slightly, but are usually around 2.1 meters off the ground for an NBA player. Generally a player performing a jump shot will jump vertically to keep the ball out of the defenders reach but the increase in projection height will also reduce the amount of vertical velocity required to make the distance to the basket. Given that the vertical distance covered will be less, the shot should also be more accurate as less force is applied to the ball to achieve the same favourable angle of entry.

                                                             (Okazaki & Rodacki, 2012)