Hello, cedwards08!
Chris, who is 6 feet tall, is walking away from a street light pole 30 feet high
at a rate of 2 ft/sec. . 
a. How fast is his shadow increasing in length when Chris is 24 ft from the pole? 30 feet? Code:
*
| *
| *
30 | | *
| 6| *
| | *
*-------*---------------*
: - x - : - - - s - - - :
From the similar right triangles: . 
Differentiate with respect to time: . )
Therefore: .  \:=\:\frac{1}{2}\text{ ft/sec})
always.
b. How fast is the tip of his shadow moving? Code:
*
| *
| *
30 | | *
| 6| *
| x | y-x *
*-------*---------------*
: - - - - - y - - - - - :
We have: . 
Differentiate with respect to time: .  )
Therefore: .  \;=\;\frac{5}{2}\text{ ft/sec})
always.
c. To follow the tip of his shadow, at what angular rate must Chris
be lifting his eyes when his shadow is 6ft long? Code:
*
| *
| * - - - - -
30 | | * θ
| 6| *
| | θ *
*-------*---------------*
: - x - : - - - s - - - :
We have: . 
Differentiate with respect to time: .  \:=\:-6s^{-2}\left(\frac{ds}{dt}\right) )
. . and we have: .  )
.[1]
We are given: . 
From (a), we have: . 
When , the right triangle is isosceles.
. . Hence: . 
Substitute into [1]: . ^2\lef t(\frac{1}{2}\right) \;=\;-\frac{1}{24})
Therefore, Chris should raise his eyes at the rate of 
radians/sec.
LinkBack URL
About LinkBacks