I don't know how to start with this problem. Please help me figure it out.
here it is :)
Navy Seal Ship A moves along towards east direction at the constant rate of 'a' meter/sec^2 while Navy Seal Ship B moves toward north at constant rate of 'b' meter/sec^2. Determine how fast the distance between them is changing when Ship A is at the coordinates of (x,0) and ship B is at the coordinates of (y,0).
On
First remember these few rules:
s= distance ;
d(s)/dt is the speed of the object;
and
second differential of distance is accelaration.
From my understanding, u firstly need to double integrate the accelaration (given in ur question) of each object at those points given to find the distance from the origin and then from there can u use Pythagorus theorem.
Assuming they start at $(0,0)$, the distance between them is given by Pythagoras' theorem : $$ f(x,y) = \sqrt{x^2+y^2} $$ So by the chain rule $$ \frac{df}{dt} = \frac{\partial f}{\partial x}\frac{dx}{dt} + \frac{\partial f}{\partial y}\frac{dy}{dt} $$ $$ = \frac{x}{\sqrt{x^2+y^2}}a + \frac{y}{\sqrt{x^2+y^2}}b $$