Asked by becca
An airplane flying west at 300 miles per hour goes over the control tower at noon, and a second airplane at the same altitude, flying north at 400 miles per hour, goes over the tower an hour later. How fast is the distance between the airplanes changing at 2:00 P.M.?
Answers
Answered by
Steve
Draw a diagram
Let the tower be at (0,0)
plane A is at distance a = 300t West after t hours
Plane B is at position b = 400(t-1) North after t hours, counting from 12:00
The distance d between the planes is given by
d^2 = (300t)^2 + (400(t-1))^2
2d dd/dt = 2(300t)(300) + 2(400(t-1))(400)
at 2:00, t=2, so
d = 200√13
400√13 dd/dt = 360000 + 320000 = 680000
dd/dt = 6800/4√13 = 1700/√13 = 471.5
feel free to check my math...
Let the tower be at (0,0)
plane A is at distance a = 300t West after t hours
Plane B is at position b = 400(t-1) North after t hours, counting from 12:00
The distance d between the planes is given by
d^2 = (300t)^2 + (400(t-1))^2
2d dd/dt = 2(300t)(300) + 2(400(t-1))(400)
at 2:00, t=2, so
d = 200√13
400√13 dd/dt = 360000 + 320000 = 680000
dd/dt = 6800/4√13 = 1700/√13 = 471.5
feel free to check my math...
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.