Mathematics, 02.11.2020 03:00 jbot9050
1. (5 points) At 6pm, ghost A is 5 kilometers due west of ghost B. Ghost A is flying west
at 15 km/hr and ghost B is flying north at 20 km/hr. How fast is the distance between
the ghosts changing at 10pm?
Answers: 1
and 
. If both ghosts moves at constant velocity such that 
and 
, then the final positions of both ghosts are, respectively:
(Eq. 1)
(Eq. 2)
is the time, measured in hours.
![\vec r_{A} = \left(-15\cdot t, 0)\,\,\,\left[km \right]](/tpl/images/0859/4027/9d317.png)
![\vec r_{B} = (5, 20\cdot t)\,\,\,\left[km\right]](/tpl/images/0859/4027/12704.png)
![\vec r_{B/A} = (5,20\cdot t)-(-15\cdot t, 0)\,\,\,[km]](/tpl/images/0859/4027/7e17c.png)
![\vec r_{B/A} =(5+15\cdot t, 20\cdot t)\,\,\,[km]](/tpl/images/0859/4027/e3b78.png)
(Eq. 3)
), measured in kilometers per hour, by implicit differentiation:
(Eq. 4)
, then the rate of change of the relative distance at 10 PM is:![\dot r_{B/A} = \frac{75+625\cdot (4)}{\sqrt{[5+15\cdot (4)]^{2}+[20\cdot (4)]^{2}}}](/tpl/images/0859/4027/fb9c8.png)
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1. (5 points) At 6pm, ghost A is 5 kilometers due west of ghost B. Ghost A is flying west
at 15 km/...
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