I/2017/9 – A particle is projected at speed u from a point O on a horizontal plane. It passes through a fixed point P which is at a horizontal distance d from O and at a height d tan β above the plane, where d > 0 and β is an acute angle. The angle of projection α is chosen so that u is as small as possible.

(i) Show that and

(ii) At what angle to the horizontal is the particle travelling when it passes through P? Express your answer in terms of α in its simplest form.

Click here for an answer (pdf).

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