SOLUTION: A person on a bicycle is 100 meters west of a person in a car. The person on the bike starts to ride at 5 meters per second directly east and at the same time the person in the car

Question 849545: A person on a bicycle is 100 meters west of a person in a car. The person on the bike starts to ride at 5 meters per second directly east and at the same time the person in the car starts to drive directly north at 20 meters per second. Use the pythagoras Theorem to write the distance between the bicycle and the car as a function of time. What is the minimum distance between the car and the bicycle? Verify that this time does give a minimum distance and find this minimum distance.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A person on a bicycle is 100 meters west of a person in a car.
The person on the bike starts to ride at 5 meters per second directly east and at the same time the person in the car starts to drive directly north at 20 meters per second.
Use the pythagoras Theorem to write the distance between the bicycle and the car as a function of time.
What is the minimum distance between the car and the bicycle?
Verify that this time does give a minimum distance and find this minimum distance.
:
let t = travel time
then
(100-5t) = bike distance from ref point
and
20t = car dist from ref point
:
d = dist between bike and car
d(t) =
d(t) =
d(t) =
Assuming the same minimum would also be for
425t^2 - 1000t + 10000
which we can simplify
17t^2 - 40t + 400
Using x = -b/(2a) to find the axis of symmetry
t =
t = 1.176 seconds minimum distance apart
:
"find this minimum distance."
Use the original pythag equation, replace t with 1.176
d(t) =
d(t) =
d(t) =
d(t) =
d(t) =
d(t) = 97 ft apart min dist
:
Graphing y = seems to confirm this

:
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