Respuesta :
Her distances and displacement are;
[tex]\begin{array}{|l|c|c|}\mathbf{Location}&\mathbf{Displacement}&\mathbf{Distance}\\&&\\a. \ Quarter \ way \ around&\dfrac{750 \cdot \sqrt{2} }{\pi} m &375 \ m\\&&\\b. \ Half \ way \ around&\dfrac{1500}{\pi} m&750 \ m\\&& \\C. \ Three \ quarter\ way \ around&\dfrac{750 \cdot \sqrt{2} }{\pi} m&1,125 \ m\\&&\\d. \ Entire \ lap&0&1,500 \ m\\\end{array}\right][/tex]
The reason the above values are correct are as follows:
The known details are:
The length of the circular track, C = 1,500 m
The required details;
Her distance and displacement at four locations starting at the top of the circle, as follows;
At the top, the starting point, the displacement = The distance = 0
a. A quarter way round the track;
The radius of the circular track, r = C/(2·π)
∴ r₁ = 1,500 m/(2·π) = (750 m)/π
The displacement a quarter way round the track, s₁² = r² + r²
∴ s₁² = ((750 m)/π)² + ((750 m)/π)²
s₁ = ((750 m)/π)·√2
The displacement a quarter way round the track, s₁ = ((750·√2)/π) m
The distance a quarter way round the track, d₁ = C/4
∴ d₁ = 1,500 m/4 = 375 m
The distance a quarter way round the track, d₁ = 375 m
b. The displacement half way around the track, s₂ = r + r
∴ s₂ = r + r = (750 m)/π + (750 m)/π = (1,500 m)/π
The distance moved half way round the circular track, d₂ = C/2
∴ d₂ = 1,500 m/2 = 750 m
The distance moved half way round the circular track, d₂ = 750 m
C. The displacement 3/4 way round the track, s₃ = s₁ = (750 m)/π)·√2
The distance moved 3/4 way round the circular track, d₃ = (3/4) × 1,500 m = 1,125 m
D. The displacement for an entire lap, which is back to starting point at the TOP, s₄ = 0
The distance traveled in one lap = The circumference of the track, C = 1,500 m
Therefore, we have the following displacement and distances at the four different locations;
[tex]\begin{array}{|l|c|c|}\mathbf{Location}&\mathbf{Displacement}&\mathbf{Distance}\\&&\\a. \ Quarter \ way \ around&\dfrac{750 \cdot \sqrt{2} }{\pi} m &375 \ m\\&&\\b. \ Half \ way \ around&\dfrac{1500}{\pi} m&750 \ m\\&& \\C. \ Three \ quarter\ way \ around&\dfrac{750 \cdot \sqrt{2} }{\pi} m&1,125 \ m\\&&\\d. \ Entire \ lap&0&1,500 \ m\\\end{array}\right][/tex]
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