Question

One car leaves a station going west at 90 kph. Another approaches the same station from the south at 70 kph. At what rate is the distance between the cars changing when the cars are each 20 km from the station?
solve using differentiation

Answer 1

dx/dt=90
dy/dt=-70 (reaching the station)
D is the distance
so
x^2+y^2=D^2
x=20 and y=20
D=\[\sqrt{x^2+y^2}\]
D*dD/dt=2x*dx/dt+2y*dy/dt
Dd/dt=(3600-2800)/\[\sqrt{800}\]

Answer 2

raziye left out a factor of 2 when taking the derivative of D^2



if we just plug in D= 20 sqrt(2) and x=20 and y= 20, dx/dt=90 and dy/dt= -70
into the derivative
\[ 2 D \frac{dD}{dt} = 2 x \frac{dx}{dt} + 2 y \frac{dy}{dt} \]