The height h (in feet) for a free-fall artifact is given by:
[tex]h(t)=-16t^2+98[/tex]
Part A:
The graph of the function is:
Part B:
To find the distance traveled from t = 0 to t = 1, we perform the subtraction:
[tex]\Delta^{0,1}_h=|h(0)-h(1)|[/tex]
Now, evaluating the function for t = 0 and t = 1:
[tex]\begin{gathered} h(0)=-16\cdot0^2+98=98 \\ h(1)=-16\cdot1^2+98=82 \end{gathered}[/tex]
Then:
[tex]\Delta^{0,1}_h=|98-82|=16[/tex]
The artifact traveled 16 feet from t = 0 to t = 1.
Part C:
h(t) is a quadratic function (non-linear), so we can conclude that the distance traveled from t = 1 to t = 2 is not the same as from t = 0 to t = 1.
To confirm this, we calculate the first distance. Evaluating the function for t = 2:
[tex]h(2)=-16\cdot2^2+98=34[/tex]
Now, the distance traveled from t = 1 to t = 2 is:
[tex]\Delta^{1,2}_h=|h(1)-h(2)|=|82-34|=48[/tex]
Which is different from the distance in part B (16 feet).
