Applied Mechanics and Graphic Statics
The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be

sin (α + β)/sin (α - β)
sin (α - β)/sin (α + β)
cos (α - β)/cos (α + β)
tan (α - β)/tan (α + β)

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Applied Mechanics and Graphic Statics
A square hole is punched out of a circular lamina, the diagonal of the square being the radius of the circle. If ‘r’ is the radius of the circle, the C.G. of the remainder from the corner of the square on the circumference will be

[r (π - 0.25)]/(π - 0.5)
[r (π + 0.25)]/(π - 0.5)
[r (π - 0.5)]/(π + 0.25)
[r (π + 0.25)]/(π + 0.5)

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