A plane flies horizontally with a speed Of 600km/h at an altitude of 10km and pasess directly over th town of quinton .find the rate at which the distance from the plane to quinton is increasing when its 20km away from quinton ?
calculus - Reiny, Sunday, March 13, 2011 at 12:22am
let the horizontal distance from Quinton be x km
let the distance between plane and Quinto by y km
x^2 + 10^2 = y^2
2x dx/dt = 2y dy/dt
dy/dt = (x dx/dt)/y
y^2 = 400 + 100 = 500
y = √500 = 10√5
dx/dt = 600 km/h
dy/dt = 20(600)/10√5 = appr. 536.7 km/h
calculus - Mehak, Sunday, March 13, 2011 at 12:42am
But did u use pythagoram theorom an how did u manipulate it ? And thanks because the answer is right .
calculus - Reiny, Sunday, March 13, 2011 at 12:51am
yes, you can see in my first line of the solution that I used the Pythagorean theorem.
I then differentiate with respect to time, since we were talking about "rates" in the question and I saw a rate given as 600 km/h
calculus - Mehak, Sunday, March 13, 2011 at 1:09am
Thank you !
calculus - Anonymous, Tuesday, January 19, 2016 at 6:17pm
how did you get dy/dt to be (x dx/dt)/y