A particle \(P\) of mass 0.5 kg is moving with velocity ( \(4 \mathbf { i } + 3 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse \(\mathbf { J }\) Ns. Immediately after receiving the impulse, \(P\) is moving with velocity \(( - \mathbf { i } + 6 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
Find the magnitude of \(\mathbf { J }\).
The angle between the direction of the impulse and the direction of motion of \(P\) immediately before receiving the impulse is \(\alpha ^ { \circ }\)