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| PAGE: 488 | SET: Exercises | PROBLEM: 65 |
The function is 
.
The fleeing object leaves the origin and moves the up 
-axis.
Substitute 
.
.
The fleeing object is travelled 
units when it is caught.
Definition Of Arc Length :
Let the function given by 
represent a smooth curve on the interval 
.
The arc length of 
between 
and 
is 
.
Where is 
.
The function is 
.
Apply derivative on each side with respect to 
.
.
Substitute 
in .
.
.
The distance travelled by pursuer is 
.
The distance travelled by fleeing object is 
.
Hence, 
.
Therefore, the pursuer has travelled twice the distance travelled by the fleeing object.
The pursuer has travelled twice the distance travelled by the fleeing object.
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