009A Sample Midterm 3, Problem 2

The position function $s(t)=-4.9t^{2}+200$ gives the height (in meters) of an object that has fallen from a height of 200 meters. The velocity at time $t=a$ seconds is given by:

$\lim _{t\rightarrow a}{\frac {s(t)-s(a)}{t-a}}$

a) Find the velocity of the object when $t=3$

b) At what velocity will the object impact the ground?

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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