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tyrique86
02.11.2020 •
Mathematics
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?
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Ответ:
The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.
Step-by-step explanation:
At first we assume that north and east directions both represent positive quantities. Let suppose that
and
. If both ghosts moves at constant velocity such that
and
, then the final positions of both ghosts are, respectively:
Ghost A
Ghost B
Where
is the time, measured in hours.
Then, the equations of motion of each ghost are, respectively:
Ghost A
Ghost B
Then, the distance between both ghosts is:
The magnitude of the relative is represented by the following Pythagorean identity:
Then, we find the rate of change of the relative distance (
), measured in kilometers per hour, by implicit differentiation:
If we know that
, then the rate of change of the relative distance at 10 PM is:
The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.
Ответ:
all of them?
Step-by-step explanation: