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An object is dropped off a building. Ignoring air resistance, the height above the ground t seconds after being droppedgiven byh(t)16 220 feet(a) Use the limit definition of the derivative to find a rate-of-change equation for the height.h'(t)feet per second(b) Use the answer to part (a) to determine how rapidly the object is falling after 2 seconds.feet per second

Question
An object is dropped off a building. Ignoring air resistance, the height above the ground t seconds after being dropped
given by
h(t)16 220 feet
(a) Use the limit definition of the derivative to find a rate-of-change equation for the height.
h'(t)
feet per second
(b) Use the answer to part (a) to determine how rapidly the object is falling after 2 seconds.
feet per second
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An object is dropped off a building. Ignoring air resistance, the height above the ground t seconds after being dropped given by h(t)16 220 feet (a) Use the limit definition of the derivative to find a rate-of-change equation for the height. h'(t) feet per second (b) Use the answer to part (a) to determine how rapidly the object is falling after 2 seconds. feet per second

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Step 1

Consider the given height function

h(t)-16/220 feet
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h(t)-16/220 feet

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Step 2

Subpart (a)

Now rate of change of the height

d(h(t)) (-16+220)
dt
dt
h'(t)=-321
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d(h(t)) (-16+220) dt dt h'(t)=-321

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Step 3

Subpart (b)

So rate of change of height will be speed in term of t...

h'(t)-32!
=-32x2
=-64 feet per second
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h'(t)-32! =-32x2 =-64 feet per second

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Math

Calculus

Derivative

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