Question
the shoreline of circle lake is a circle with diameter 2 mi.nancy's training routine begins at point e on the eastern shore of the lake.she jogs along the north shore to a point p and then swims the straight line distance,if any point ,from point to point w diametrically opposite.nancy swims at a rate of 2 mi/h and josh 8 mi/h how far should nancy jog in order to complete her training routine?what is the least and greatest amount of time answer?
Answers
Steve
Label the center of the circle O. Circle O has radius 1.
If angle EOP is θ, then she
jogs a distance of rθ = θ
swims a distance of r sin(π-θ)/2 = r sin(π/2-θ/2) = r cos(θ/2) = cos θ/2
so, since time = distance/speed, her time is
t(θ) = θ/8 + 1/2 cos(θ/2)
To find min/max, set dt/θ = 0 and solve for θ.
If angle EOP is θ, then she
jogs a distance of rθ = θ
swims a distance of r sin(π-θ)/2 = r sin(π/2-θ/2) = r cos(θ/2) = cos θ/2
so, since time = distance/speed, her time is
t(θ) = θ/8 + 1/2 cos(θ/2)
To find min/max, set dt/θ = 0 and solve for θ.