Sol. Using the coordinate system shown in the figure, the motion of the stone can be described by the following relations:

x = v 0 tcos α , y = v 0 t sin α – t 2 ,

v x = v 0 cos α , v y = v 0 sin α – gt

The stone is at the greatest distance from the origin when its velocity is perpendicular to its position vector. The condition for this is

= ,

Which yields a quadratic equation for the time t at which this happens;

t 2 – t + = 0.

If this is not to happen, the discriminant of this equation must be negative i.e.,

< 4 .

Thus, for the stone to the permanently moving away from the thrower, we must have
sin α < = 0.94. i.e. α < 70.5º.