Question

Two boats sail away from a buoy making a 90 degree angle. The first boat is 165 meters away and is traveling at 25 m/s. The second boat has been traveling at 35 m/s for pi mINUTES. What is the rate of change in distance between the two boats?

Answer 1

Answer:

Step-by-step explanation:

lets say in the shown triangle x=165

so speed $\frac{dx}{dt} =25$

and  $\frac{dy}{dt} =35$

Also since distance = speed* time

time = pi minutes = pi/60 seconds

y = $\frac{35\pi \pi }{60}$

y = $\frac{7\pi }{12}$

Now using the pythagorean :

$x^2+y^2=z^2\\so \\165^2+(\frac{7\pi }{12} )^2 =z^2$

derivate the equation so  we get :

$x\frac{dx}{dt} +y\frac{dy}{dt} =z\frac{dz}{dt}$$165*25+35*\frac{7\pi }{12}=\sqrt{165^2+(\frac{7\pi }{12})^2} *\frac{dz}{dt}$

$\frac{dz}{dt} =25.387$ m/s

So Rate of change = 25.387 m/s