Better Students Ask More Questions.
Two aircraft approach airfield at the same constant altitude. The first aircraft is...
Two aircraft approach airfield at the same constant altitude. The first aircraft is moving S at 250km/h while the second is moving W at 600 km/h-----
At what rate is the distance between them changing when the first aircraft is 60 km from the field and the second is 25km from the field.
1 Answer | add yours
High School Teacher
The two aircraft form a right triangle with the right ange at the airport.
Suppose the westbound aircraft distance from the airport is x and the southbound aircraft distance is y. Then we can find the distance between the aircraft using the Pythagorean Theorem.
`s^2 = x^2 + y^2`
Now we need to implicitly differentiate with respect to time to get
` 2s(ds)/(dt) = 2x(dx)/(dt) + 2y(dy)/(dt)`
Now `(dx)/(dt) = -600 "km/hr"` and `(dy)/(dt) = -250 "km/hr"` if we consider this on a coordinate plane.
So `(ds)/(dt) = (x(dx)/(dt) + y(dy)/(dt))/s`
The first aircraft (y) is 60km and (x) is 25km.
`(ds)/(dt) = (25(-600)+(60)(-250))/(sqrt(60^2+25^2)) ~~ -462 "km/hr"`
Posted by beckden on May 12, 2012 at 3:57 AM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.