Page 147 - How To Solve Word Problems In Calculus
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SOLUTION
Let x represent the (straight-line) distance between the
runner and the trainer and let s represent the distance run
around the track.
R
100 s
x
θ
T
O 100
The angle formed by the two radii as shown in the diagram is
labeled θ.
ds dx π
Given: = 10 Find: when θ =
dt dt 2
By the law of cosines,
2
2
2
x = 100 + 100 − 2(100)(100) cos θ
2
x = 20,000 − 20,000 cos θ
Differentiating,
dx dθ
2x = 20,000 sin θ
dt dt
dx dθ
x = 10,000 sin θ
dt dt
dx π dθ
To compute when θ = , we need the values of x and .
dt 2 dt
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