Essay On Math And Basketball

Modeling Mathematics and Basketball

Rationale:

One day I was watching basketball game in my school in which five out of ten players were my friends. When the game started it was so thrilling and excited, players are running on the entire court and it was full of energy and stamina. At there I listened the word “Buzzer Beater” this is the shot that is converted and decides who is winning team is. Then and there only I decided to opt my topic on modeling mathematics and basketball. After that I discussed with my teacher and she approved the topic.

Introduction:

Basketball is very popular game and it is played in many countries in the world. It is played at school level collage level and professional level also it is a fast scoring game and it requires stamina and strength of the

When there is no air resistance and not any change in the gravitational acceleration, situation is described Ideal projectile. This is a close approximation of actual projectile motion of mathematics where distances are travelled very small.

Mathematical Presentation:

Derivations

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Range of a projectile

The horizontal position of the projectile is

X(t) = v t cosθ

In the vertical direction y(t) = v t sinθ - 1/2 g t2

when the projectile returns to the same height it originated. Let t be any time when the height of the projectile is equal to its initial value.

0 = v t sinθ - 1/2 g t2

By factoring: t = 0 t = 2vsinθ/g

Plugging this value for (t) into the horizontal equation yields

X = (2V^2 cosθ sinθ)/g

Sin 2θ = 2 sin θ cos θ

Therefore simplify the solution