86fed3dc-de34-47e4-bb18-795d1fb212f2 21 Norm Schutzkus 4 5 false false 0 decimal

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Circle swimming is an amazing aquatic technique in which an athlete can swim as fast on any curved path as they can on a straight one. The size of the lake was carefully calibrated to the athlete’s fastest swimming speed, which was 1 unit distance over 1 time unit.

r.Lake 3.5 :

The lake’s radius measured 3.5 units in length

∴

C.Lake 2 π * r.Lake * : 21.9911

The lake's circumference

ω Δθ Δt / ≡

3.5 units of time to swim one full radius

Δt 3.5 :

he took exactly 3.5 units of time to swim one full radius.

Δθ 3.5 :

One revolution

ω Δθ Δt / : 1

athlete’s fastest swimming speed, which was 1 unit distance over 1 time unit.

v.Swim ω C.Lake * : 21.9911

v.Bear v.Swim 3.5 * : 76.969

bear was on the slow side, its running speed was still 3.5 times as fast as he could swim.

r.Bear r.Lake :

Divide the linear velocity by the circumference to get the angular velocity (in rotations per unit time.

Thus initally:

ω.Swim v.Swim C.Lake / : 1

ω.Bear v.Bear C.Lake / : 3.5

At what circumference will the swimmer's angular velocity equal the bear's maintaining a position diametrically opposite the bear?

ω.Swim1 ω.Bear ≡

ω.Swim1 v.Swim C.Lake ω.Bear / / : 3.5

ω.Swim ω.Bear * 3.5

Swimmer's circumference maintaining a diametrically oppositeposition to the bear's angular velocity C.Swim C.Lake ω.Swim1 / : 6.2832

r.Swim C.Swim 2 π * / : 1