Geometry: I want to understand some points

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To find the unknown x related to an arc of a great circle 10 units long receding from its chord, the relationship between the radius R and angle alpha is crucial. The discussion suggests that x can be expressed as R - R cos(alpha), representing the maximum distance between the arc and the chord. The geometry involves an isosceles triangle formed by the endpoints of the arc and the center of the circle. Additionally, properties of triangles indicate that the angle can be determined to be 45 degrees, leading to R being calculated as the square root of 50. Understanding these relationships is essential for solving the problem effectively.
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What is my unknown (say x) if I am finding the value in which an arc of a great circle 10 units long recedes from its chord? (given radius R and angle alpha?)

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I am guessing, you can express R = xR + (1-x)R where (1-x)R is the height of your (isosceles) triangle and xR is the bit from the chord to the circle.
 
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What do you mean by "recedes from its chord"?
 
HallsofIvy, seems like the arc is moving away from its respected chord (form by the two enddpoints of the arc)

My friend told me that x = R - R cos (alpha)... I wonder why...
 
He has given the greatest distance between the arc and the chord i.e. the difference of the radius and distance of the chord from the center
 
hi
By using the laws properties of triangle you will get the angle to be 45 degrees and
R to be square root of 50

http://www.mathsrevision.net/gcse/pages.php?page=47
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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