Question #cd6e9

1 Answer
Jan 21, 2018

-1290 mph

Explanation:

At this particular instant we have:

MFDocsMFDocs

We are told that:

sf(dy/dt=-600color(white)(x) "mph")

sf(dx/dt=-450color(white)(x)"mph")

We are asked to find sf((dr)/dt)

At any particular instant we can use Pythagoras to find the relationship between these variables:

sf(y^2+x^2=r^2)

Differentiating implicitly with respect to t:

sf(D(x^2+y^2)=D(r^2)

:.sf(2y.dy/dt+2x.dx/dt=2r.(dr)/dt)

Putting in the numbers:

sf((2xx200xx-600)+(2xx150xx-450)=2xx250.(dr)/dt)

sf(-240,000-405,000=500.(dr)/dt)

sf((dr)/dt=-(645,000)/500=-1290color(white)(x)"mph")