Question
1. Plane A is 40 mi south and 100 mi east of Plane B. Plane A is flying 2 miles west for every mile it flies north, while Plane B is flying 3 mi east for every mile it flies south.
a. Where do their paths cross?
b. Which plane must fly farther?
c. What ratio of the speed of Plane B to the speed of Plane A would
produce a midair collision?
a. Where do their paths cross?
b. Which plane must fly farther?
c. What ratio of the speed of Plane B to the speed of Plane A would
produce a midair collision?
Answers
Start by drawing a diagram of the situations, such as:
http://img101.imageshack.us/img101/3371/newt.jpg
a. The point where the two paths cross is at (-40,20) relative to plane A. (Check my graphical solution).
b. not sure what exactly is requested.
Either plane A can fly further south, or plane B a little further north, or they can avoid each other by changing altitudes.
c. The deadly ratio can be found by calculating the distances of each plane from the intersection point (-40,20). If the speeds are inversely proportional to the distance, it is likely to have a mid-air collision.
http://img101.imageshack.us/img101/3371/newt.jpg
a. The point where the two paths cross is at (-40,20) relative to plane A. (Check my graphical solution).
b. not sure what exactly is requested.
Either plane A can fly further south, or plane B a little further north, or they can avoid each other by changing altitudes.
c. The deadly ratio can be found by calculating the distances of each plane from the intersection point (-40,20). If the speeds are inversely proportional to the distance, it is likely to have a mid-air collision.