Applied Mechanics and Graphic Statics
For the given values of initial velocity of projection and angle of inclination of the plane, the maximum range for a projectile projected upwards will be obtained, if the angle of projection is

α = π/4 - β/2
α = π/4 - β/2
α = π/2 + β/2
α = β/2 - π/2

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Applied Mechanics and Graphic Statics
‘u₁’ and ‘u₂’ are the velocities of approach of two moving bodies in the same direction and their corresponding velocities of separation are ‘v₁’ and ‘v₂’. As per Newton's law of collision of elastic bodies, the coefficient of restitution (e) is given by

e = v₁ - v₂/u₂ + u₁
e = v₁ - v₂/u₂ - u₁
e = u₂ - u₁/v₁ - v₂
e = v₂ - v₁/u₁ - u₂

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Applied Mechanics and Graphic Statics
Varingon’s theorem of moment’s states

Algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point
Arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point

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