Question

Calculus question. Pls help.

Answer 1

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

`(s_A)^2+(s_B)^2=s^2` where s is distance between

when sA=sB=100, then find speed of change in distance

first find distance

`100^2+100^2=s^2`

`d=100√(2)`

if we look at
`(s_A)^2+(s_B)^2=s^2` and take the derivitive of both side with respect to time, we get

`2(s_A)(ds_A)/(dt)+2(s_B)(ds_B)/(dt)=2(s)(ds)/(dt)`

`(ds_A)/(dt)` is speed of plane A

`(ds_B)/(dt)` is speed of plane B

we are solving for
`(ds)/(dt)`

subsituting

`2(100)(450)+2(100)(275)=2(100√(2))(ds)/(dt)`

solving

`(ds)/(dt)=512.652`