A particle which is projected from the origin with initial speed ms^-1 at an angle of to the positive -axis lands on the -axis, as shown in the diagram. The particle is subject to an acceleration due to gravity of ms^-1. 
 

The position vector of the particle, , where is the time in seconds after the particle is projected, is given by

.     (Do NOT prove this.)

For some value(s) of    there will be two times during the time of flight when the particle’s position vector is perpendicular to its velocity vector.

Find the value(s) of    for which this occurs, justifying that both times occur during the time of flight.  (5 marks)