Question

how do i get 36 mph out of this?

two cars start moving from the same point. one travels north at 20 mi/h and the other travels east at 30 mi/h. At what rate is the distance between the two cars increasing 2 hours later?

Answer 1

I have tried x^2+y^2=z^2

2(60)(30)+2(40)(20)= 2( ) dz/dt
im stuck here

Answer 2

\[x^{2}+y^{2}=z^{2}\]Use implicit differentiation:\[2x\frac{dx}{dt} +2y\frac{dy}{dt}=2z\frac{dz}{dt}\]Solve for dz/dt:\[\frac{dz}{dt}=\frac{x\frac{dx}{dt} + y\frac{dy}{dt}}{z}\]You are given (dx/dt)=30mi/h, (dy/dt)=20mi/h, x= (30 * 2)=60, and y = (20*2)=40. For z, you can solve the original equation for it and then substitute:\[\frac{dz}{dt}=\frac{x\frac{dx}{dt} + y\frac{dy}{dt}}{\sqrt{x^{2}+y^{2}}}\] Then plug in your values and solve:\[\frac{dz}{dt}=\frac{(60)(30) + (40)(20)}{\sqrt{(60)^{2}+(40)^{2}}} \] \[\frac{dz}{dt}=\frac{2600}{\sqrt{5200}} = 10\sqrt{13} \approx 36.055\]

Answer 3

thanks very much