To determine the best fit model for the data you described, we typically analyze the relationship between the time (in seconds) and the height (in feet) of the balls thrown from the building.
Since the balls are projected from a height and descend under the influence of gravity, the height of the balls as a function of time can be described by a quadratic equation. This is due to the fact that the motion of an object under the influence of gravity follows a parabolic trajectory.
Here's how you can proceed to find the best fit model:
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Quadratic Model: Since the problem involves projectile motion, a quadratic equation of the form: \[ h(t) = -kt^2 + vt + h_0 \] would typically be the best fit, where:
- \( h(t) \) is the height at time \( t \)
- \( k \) is a constant that depends on the initial velocity and gravity
- \( v \) is the initial vertical velocity
- \( h_0 \) is the initial height (35 feet in this case)
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Examine the Data: Look at the scatterplot you mentioned. If the points resemble a parabolic curve (opening downwards, since the balls are falling), then a quadratic model is appropriate.
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Fit the Model: You can use regression analysis (specifically polynomial regression) on your data points to find the coefficients for the quadratic model. Many software tools can help with this, such as Python’s NumPy and Matplotlib libraries, Excel, or graphing calculators.
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Validation: Once you establish a quadratic model, plot it alongside your data points to see how well it fits. Look for how closely the predicted heights match the observed heights at various time points.
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Alternative Models: If, for some reason, the scatterplot appears linear or another type of function (exponential or logarithmic), you might need to consider those models. However, for projectile motion, a quadratic function is typically the most suitable.
In conclusion, based on the description you're giving about projectile motion from a height, a quadratic model is likely the best fit for the scatterplot data you have.