Question taken from one of the O-level papers (Additional Mathematics I):
Take 'g' to be 9.8 metres per second per second.
If you use a slide-rule, write "S.R." against any result so obtained.
Two particles are projected simultaneously from the same point with the same speed of 25m/s.
Particle P is projected vertically.
Particle Q is projected at an angle A with the horizontal such that cosA = 0.6.
Prove that, as long as both particles are in the air, the line PQ is constant in direction.
(I believe we're supposed to assume no air resistance.)
If you want extra kudos, work it out for the generic case with initial speed v and angle A.