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. Author manuscript; available in PMC: 2018 Jul 5.
Published in final edited form as: J Biomech. 2017 May 31;59:90–100. doi: 10.1016/j.jbiomech.2017.05.019

Figure 2.

Figure 2

Calculation of the final hand endpoint velocity vector (v⃗f ) necessary for a successful free throw. As this throw is well modeled as a ballistic problem, the independent variables are the angle of release (α) and the distance of the ball’s center from the basket’s center (Δx, Δy). (a) Utilizing the anthropometric geometric model described in Eq. 1, a player’s height and the joint angles at the point of release are utilized to find the position of the hand endpoint relative to the shoulder joint (designated here as the origin). (b) The radius of the ball and the parameters of the basket (i.e. height of the basket and horizontal distance of the shoulder joint to the basket’s center) are incorporated to find the necessary displacement parameters (Δx, Δy). (c) Utilizing these displacements and the angle of release (α), ballistics equations are rearranged and used to solve for the necessary release velocity vector for a successful free throw.