call eastward plane A and westward plane B
speed from west is 450
speed from south is 275
the distance between them is defined by pythagorean theorem
[tex](s_A)^2+(s_B)^2=s^2[/tex] where s is distance between
when sA=sB=100, then find speed of change in distance
first find distance
[tex]100^2+100^2=s^2[/tex]
[tex]d=100\sqrt{2}[/tex]
if we look at [tex](s_A)^2+(s_B)^2=s^2[/tex] and take the derivitive of both side with respect to time, we get
[tex]2(s_A)\frac{ds_A}{dt}+2(s_B)\frac{ds_B}{dt}=2(s)\frac{ds}{dt}[/tex]
[tex]\frac{ds_A}{dt}[/tex] is speed of plane A
[tex]\frac{ds_B}{dt}[/tex] is speed of plane B
we are solving for [tex]\frac{ds}{dt}[/tex]
subsituting
[tex]2(100)(450)+2(100)(275)=2(100\sqrt{2})\frac{ds}{dt}[/tex]
solving
[tex]\frac{ds}{dt}=512.652[/tex]
