
a.
To find : The instantaneous velocity of the arrow after one second.
a.

Answer to Problem 28E
The instantaneous velocity of the arrow after one second is 56.34m/s.
Explanation of Solution
Given information:
The arrow is shot upward on the moon with a velocity of 58m/s, its height after t seconds is given by
Calculation :
The instantaneous velocity after one second is the derivative of the function
The derivative of a function
provided this limit exist.
According to definition, the derivative of
Hence,
The instantaneous velocity of the arrow after one second is 56.34m/s.
b.
To find : The instantaneous velocity of the arrow when
b.

Answer to Problem 28E
The instantaneous velocity on the arrow when
Explanation of Solution
Given information:
The arrow is shot upward on the moon with a velocity of 58m/s, its height after t seconds is given by
Calculation :
The instantaneous velocity at
The derivative of a function
provided this limit exist.
According to definition, the derivative of
Hence,
The instantaneous velocity on the arrow when
c.
To find : The time t when the arrow hit the moon.
c.

Answer to Problem 28E
Arrow will hit the moon at time
Explanation of Solution
Given information:
The arrow is shot upward on the moon with a velocity of 58m/s, its height after t seconds is given by
Calculation :
The arrow will hit the moon when
Therefore,
Since, at
Hence,
Arrow will hit the moon at time
d.
To find : The velocity with what the arrow will hit the moon.
d.

Answer to Problem 28E
Arrow will hit the moon at time
Explanation of Solution
Given information:
The arrow is shot upward on the moon with a velocity of 58m/s, its height after t seconds is given by
Calculation :
From (b) the instantaneous velocity on the arrow when
Also, the time at which arrow will hit the moon is
To find the velocity with what the arrow will hit the moon, substitute
Hence,
The velocity at which the arrow will hit the moon is 58 m/s.
Chapter 13 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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