Concept explainers
(a).
To calculate: The formula for the instantaneous rate of change of the balloon.
(a).
Answer to Problem 72E
The formula of instantaneous rate of change of the balloon is
Explanation of Solution
Given information: The displacement s,
Formula used:
Differentiate the equation of displacement ( s ) with respect to
Calculation:
Hence, the equation of rate change of the balloon is
(b).
To calculate: Average rate of change of the balloon after the first three seconds.
(b).
Answer to Problem 72E
The average speed is 16 feet per second.
Explanation of Solution
Given information: The displacement s,
Formula used:
Calculation:
Total distance after two second:
Total time, when
Therefore,
Hence, total time,
Therefore,
Hence, the average speed after two second is 20.43 feet per second.
(c).
To calculate: The velocity of the coin as it hit the ground.
(c).
Answer to Problem 72E
The velocity of the coin as it hit the ground is 32.32 feet per second.
Explanation of Solution
Given information: The displacement s,
Coin will impact the ground, when
Therefore,
Calculation:
Hence,
Formula used:
Differentiate the equation of displacement ( s ) with respect to
Put,
Hence, velocity at time of impact is 32.32 feet per second.
(d).
To calculate: The time when the coin`s velocity − 70 feet per second.
(d).
Answer to Problem 72E
At 2.19 seconds the velocity of the coin is -70 feet per second.
Explanation of Solution
Given information: The displacement s,
To get the velocity, differentiate the equation of displacement ( s ) with respect to
Formula used:
Differentiate the equation of displacement ( s ) with respect to
Put,
Therefore, in 2.19 seconds, the velocity of the coin is -70 feet per second.
(e).
To draw: a graph to verify the result of parts (a) and (b)
(e).
Answer to Problem 72E
The required graph:
Explanation of Solution
Given information: The displacement s,
The above
Therefore, it takes
If
Calculation:
Hence,
It means the height of the coin from the ground just before throwing, since the initial is 120 feet.
Chapter 11 Solutions
Precalculus with Limits: A Graphing Approach
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