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Related rate problem?
A 6-ft-tall person walks away from a 10-ft lamppost at
a constant rate of 3 ft/sec. What is the rate that the tip of the shadow moves away from the pole when the person is
10 ft away from the pole?
Please explain the steps so I can understand how to do this problem :)
1 Answer
- SqdancefanLv 74 years agoFavorite Answer
Step 1: draw a diagram. Assign variables to the points of interest--the position of the person, the position of the shadow tip.
Step 2: write equations relating the variables of step 1.
Step 3: solve for the rate of change of the position of the shadow tip (wanted to find) as a function of the rate of change of the position of the person (given).
_____
If x is the distance of the person from the lamppost, and s is the distance of the shadow tip from the lamppost, then
.. (10 -6)/x = 10/s
.. s = 2.5x
Then the rates of change are
.. s' = 2.5x' = 2.5*(3 ft/s) = 7.5 ft/s . . . . . independent of distance from the pole.
The tip of the shadow is moving at 7.5 ft/s.
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In "ft/s", the "s" stands for units of seconds. It should not be confused with the variable "s" used to represent the length of the shadow. A better choice of variable would avoid any problem.
