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A little history: Massachusetts physical education teacher James Naismith invented basketball in the late 1800s to keep his class occupied indoors in bad weather. He used a peach basket and a ball like a soccer ball.
Activity
For a free throw shot in basketball (in US standard units):
the free throw line is 15 ft away from the foot of the basket
the basket is 10 ft above the ground
the player releases the ball from an approximate height of 8 ft
Find two different functions tha could model the shot into the basket. Make sure that each function satisfies the specifications.
Decide on the form of the quadratic function that is most appropriate for your models, and give reasons for your choice of form.
From your two models, select the one that you think best models a real-life shot. Explain why.
Your model does not take into account some factors that affect the path of the ball, or whether the shot goes into the basket. Suggest what some of these factors might be.
A player from the opposing team could intercept the ball on its way to the basket. Assume that an opposing player is 5 ft away from the free thrower and can jump to reach a maximum of 10 ft. Could this player intercept the ball in your model? If so, modify your function so that it models the ball reaching the basket.
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