Solved problem: Acceleration in a basketball throw

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Statement

difficulty

A basketball player throws the ball with a velocity of ${\vec{v}}_{1} = - 2 \cdot \vec{i} + \vec{j} m / s$ , with such bad luck that it bounces off the board with a velocity ${\vec{v}}_{2} = 15 \cdot \vec{i} + 3 \cdot \vec{j} m / s$ .

Calculate the average acceleration knowing that the impact against the board lasts exactly 0.02 seconds

Solution

Data

${\vec{v}}_{1} = - 2 \cdot \vec{i} + \vec{j} m / s$
${\vec{v}}_{2} = 15 \cdot \vec{i} + 3 \cdot \vec{j} m / s$
Δt=2 s

Resolution

To calculate the average velocity, we must use the following equation:

{\vec{a}}_{a} = \frac{{\vec{v}}_{2} - {\vec{v}}_{1}}{t_{2} - t_{1}} = \frac{∆ \vec{v}}{∆ t}

We already know Δt, then we can calculate $∆ \vec{v}$ :

$Δ \vec{v} = \vec{v_{2}} - \vec{v_{1}} = (15 - (- 2)) \cdot \vec{i} + (3 - 1) \cdot \vec{j} \Rightarrow Δ \vec{v} = 17 \cdot \vec{i} + 2 \cdot \vec{j}$

Substituting into the first equation, we will calculate the average acceleration:

$\vec{a_{a}} = \frac{17 \cdot \vec{i} + 2 \cdot \vec{j}}{0.02} \Rightarrow \vec{a_{a}} = (850 \cdot \vec{i} + 100 \cdot \vec{j}) m / s^{2}$

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

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{\vec{a}}_{a} = \frac{{\vec{v}}_{2} - {\vec{v}}_{1}}{t_{2} - t_{1}} = \frac{∆ \vec{v}}{∆ t}

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Acceleration in a basketball throw

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