A helicopter is 400 miles directly north of Ghana and is flying at 20 miles per hour. A second helicopter is 300 miles east of Ghana and is flying west at 15 mph. What is the rate of change of the distance between the helicopters?
math - Reiny, Thursday, December 30, 2010 at 6:23pm
You don't say which way the first helicopter is flying, north or south or ...
I will assume it is flying south.
Make a right-angled triangle with y as the remaining distance to Ghana and x as the remaining distance.
let d be the distance between them
d^2 = y^2 + x^2
2d dd/dt = 2ydy/dt + 2xdx/dt
when x=300 and y = 400
d^2 = 300^2 + 400^2
d = 500 (did you recognize the 3,4, 5 triangle ?)
dd/dt = (400(-20) + 300(-15))/(2(500)) = 12.5