A ball of mass \(\SI{10}{\kilo\gram}\) hits a smooth horizontal surface with speed \(\SI[per-mode=symbol]{10\sqrt 2}{\meter\per\second}\) at an angle of \(45^\circ\). The coefficient of restitution between the ball and surface is \(\epsilon = \SI{0.5}{}\) and the ball remains in contact with the surface for \(\SI{0.1}{\second}\). Let \(F\) be the instantaneous force exerted by the ball at any time during the collision.

Find the average value of the force, given by \(\langle F \rangle\) in \(\si{\newton}\).

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