Projectile motion and equilibrium of a rigid body

Learning objectives

Resolve the motion of a projectile into independent horizontal and vertical components, with constant horizontal velocity u cos α and vertical acceleration −g, and derive the trajectory equation y = x tan α − gx²/(2u²cos²α)

Calculate the time of flight, the greatest height u²sin²α/(2g) and the horizontal range u²sin 2α/g for launch from level ground, and show that the range is greatest when α = 45°

Find the two angles of projection that produce a given range, explaining why they are complementary, and solve problems where the projectile lands at a different level from the point of projection

Locate the centre of mass of a uniform lamina or a composite rigid body by taking moments of the parts about two perpendicular axes, using the standard results for a triangle, a circular sector and a circular arc, together with those for a solid cone, a solid hemisphere and a hemispherical shell

Apply the two conditions for equilibrium of a rigid body, that the vector sum of the forces is zero and that the sum of the moments about any point is zero, to find unknown forces, reactions and distances

Decide whether a body resting on a rough inclined surface will slide or topple first by comparing the angle of friction arctan μ with the angle at which the line of action of the weight passes outside the base