6.1.2 Steph Curry Model

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 6.1 Linear Combination of Vectors

Properties: N/A
Sufficiencies: N/A
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Model of Steph Curry's Free Throw

Let's analyze Steph Curry's shooting technique for free throws. Below, we have a diagram that demonstrates the typical trajectory of Curry's free-throws.
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From our study of physics, we can model the trajectory of the basketball using the function

h (x) = a_{0} \cdot 1 + a_{1} \cdot x + a_{2} \cdot x^{2} .

Suppose the coefficient values of this polynomial are given by

\begin{aligned} a_{0} = 7.2500, & a_{1} = 1.5610, & a_{3} = - 0.0975 \end{aligned}

Then, we can find the set of points in this output given by:

\begin{aligned} [\begin{array}{c} h_{1} \\ h_{2} \\ h_{3} \end{array}] & = [\begin{array}{c} 7.2500 \cdot 1 + 1.5610 \cdot 0 + - 0.0975 \cdot 0^{2} \\ 7.2500 \cdot 1 + 1.5610 \cdot 8 + - 0.0975 \cdot 8^{2} \\ 7.2500 \cdot 1 + 1.5610 \cdot 14 + - 0.0975 \cdot 14^{2} \end{array}] \\ = 7.2500 \cdot [\begin{array}{c} 1 \\ 1 \\ 1 \end{array}] + 1.5610 \cdot [\begin{array}{c} 0 \\ 8 \\ 14 \end{array}] + - 0.0975 \cdot [\begin{array}{c} 0 \\ 64 \\ 196 \end{array}] \\ = [\begin{array}{c} 7.2500 \\ 13.498 \\ 9.9994 \end{array}] \end{aligned}

Remark. This problem be rewritten as a 10 Matrix-Vector Multiplication problem.

[\begin{matrix} 1 & 0 & 0 \\ 1 & 8 & 64 \\ 1 & 14 & 196 \end{matrix}] [\begin{matrix} 7.25 \\ 1.561 \\ - 0.0975 \end{matrix}] = [\begin{matrix} 7.2500 \\ 13.498 \\ 9.9994 \end{matrix}]

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