15. A football was thrown upward and allowed to fall back to the ground. Mark gathered the data below about the height of the football at different intervals after it was thrown. Time (seconds) & Height (feet) 0.0 & 56.0 0.5 & 67.5 1.0 & 71.4 1.5 & 68.1 2.0 & 56.2 2.5 & 36.0 3.0 & 7.9 According to Mark's data, what was the approximate height of the object after 2.2 seconds?

Question

15. A football was thrown upward and allowed to fall back to the ground. Mark gathered the data below about the height of the football at different intervals after it was thrown. Time (seconds) & Height (feet) 0.0 & 56.0 0.5 & 67.5 1.0 & 71.4 1.5 & 68.1 2.0 & 56.2 2.5 & 36.0 3.0 & 7.9 According to Mark's data, what was the approximate height of the object after 2.2 seconds?

Answer 1

#Explanation#The data provided is a set of discrete points in time and the corresponding height of the football. To estimate the height of the football at a time not explicitly given in the data (2.2 seconds), we can use interpolation. Interpolation is a method of constructing new data points within the range of a discrete set of known data points.In this case, 2.2 seconds falls between the time points 2.0 and 2.5 seconds. We can use these two points to estimate the height at 2.2 seconds.The formula for linear interpolation is:

where:-

is the point at which we want to estimate the value (2.2 seconds in our case),-

and

are the x-values of the data points our x falls between (2.0 and 2.5 seconds),-

and

are the y-values of the data points our x falls between (56.2 and 36.0 feet).#Answer#Substituting the known values into the formula, we get:

This simplifies to:

And further simplifies to:

So, the approximate height of the football at 2.2 seconds is 48.12 feet.

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