Answer :
A sailboat is traveling east form a point p at a rate of 20 km/hr and a motorized boat starts 300 km north of point p and is traveling south at a rate of 35 km/hr. The distance between the boats changing 3 hours later is 37.55 km/hour.
In the given question,
A sailboat is traveling east form a point p at a rate of 20km/hr.
A motorized boat starts 300 km north of point p and is traveling south at a rate of 35 km/hr.
We have to find how fast the distance between the boats is changing 3 hours later.
Solution
Given that
x=20(3)=60
y=300+(35)(3)=405
Using Pythagoras theorem
X^2+y^2=z^2
z = √60^2+405^2
z=409.5
We also have dx/dt=20 and dy/dt=300
Using
X^2+y^2=z^2
Differentiate w.r.t time
d/dt (x^2) + d/dt (y^2) = d/dt (z^2)
2xdx/dt+2ydy/dt = 2zdz/dt
dz/dt = 1z(xdx/dt+ydy/dt)
dz/dt = 1/409.5(60(20)+35(405))
dz/dt = 37.5
Distance is changing 37.55 km/hour.
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