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Answer 1 · 2018-01-21T14:24:31

-1290 mph

At this particular instant we have:

MFDocs

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")#