Suppose the wind is blowing with force vector F = (-y, 2x) in the vicinity of a straight road segment C from the point (0,0) to the point (4,3). A car moves along the straight road in two different scenarios: • there are traffic lights along the road segment causing the car to slow down and speed up again in such a way that its position along the road is given by r₁(t) = 2t 4 π sin 3t, 3t 2π sin 3t for 0 ≤ t ≤ 2π; • The traffic lights are broken and the car moves along the road segment at constant speed so that its position is given now by r₂(t) = (4t, 3t)

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Chapter1: Units, Trigonometry. And Vectors
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Suppose the wind is blowing with force vector F = (-y, 2x) in the vicinity of a
straight road segment C from the point (0,0) to the point (4,3). A car moves along the
straight road in two different scenarios:
there are traffic lights along the road segment causing the car to slow down and speed up
again in such a way that its position along the road is given by
for 0≤ t ≤ 2π;
• The traffic lights are broken and the car moves along the road segment at constant speed
so that its position is given now by
for 0 ≤ t ≤ 1.
4
3t
ri(t) - (²-sin 3f, 2-sin 3t)
3
r₂(t) = (4t, 3t)
Use each parametrization separately to determine the total work done by the wind on the car
during its journey and show that (strangely?) it is the same in both scenarios.
F. dr.
Remark: Recall that the work done by a vector field F along a path C is just the line integral
[F
Transcribed Image Text:Suppose the wind is blowing with force vector F = (-y, 2x) in the vicinity of a straight road segment C from the point (0,0) to the point (4,3). A car moves along the straight road in two different scenarios: there are traffic lights along the road segment causing the car to slow down and speed up again in such a way that its position along the road is given by for 0≤ t ≤ 2π; • The traffic lights are broken and the car moves along the road segment at constant speed so that its position is given now by for 0 ≤ t ≤ 1. 4 3t ri(t) - (²-sin 3f, 2-sin 3t) 3 r₂(t) = (4t, 3t) Use each parametrization separately to determine the total work done by the wind on the car during its journey and show that (strangely?) it is the same in both scenarios. F. dr. Remark: Recall that the work done by a vector field F along a path C is just the line integral [F
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