1. \hspace{0pt} [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal perpendicular unit vectors.]

A particle \(P\) is moving with velocity ( \(4 \mathbf { i } - \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\) on a smooth horizontal plane. The particle collides with a smooth vertical wall and rebounds with velocity \(( \mathbf { i } + 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) The coefficient of restitution between \(P\) and the wall is \(e\).

1. Find the value of \(e\). After the collision, \(P\) goes on to hit a second smooth vertical wall, which is parallel to \(\mathbf { i }\).
   The coefficient of restitution between \(P\) and this second wall is \(\frac { 1 } { 3 }\)
   The angle through which the direction of motion of \(P\) has been deflected by its collision with this second wall is \(\alpha ^ { \circ }\).
2. Find the value of \(\alpha\), giving your answer to the nearest whole number.