5. A particle of mass 0.5 kg is moving on a smooth horizontal surface with velocity \(12 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it receives an impulse \(K ( \mathbf { i } + \mathbf { j } ) \mathrm { N } \mathrm { s }\), where \(K\) is a positive constant. Immediately after receiving the impulse the particle is moving with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a direction which makes an acute angle \(\theta\) with the vector \(\mathbf { i }\). Find

1. the value of \(K\),
2. the size of angle \(\theta\).