- A particle \(P\) has mass 0.5 kg . It is moving in the \(x y\) plane with velocity \(8 \mathbf { i } \mathrm {~ms} ^ { - 1 }\) when it receives an impulse \(\lambda ( - \mathbf { i } + \mathbf { j } )\) Ns, where \(\lambda\) is a positive constant.
The angle between the direction of motion of \(P\) immediately before receiving the impulse and the direction of motion of \(P\) immediately after receiving the impulse is \(\theta ^ { \circ }\)
Immediately after receiving the impulse, \(P\) is moving with speed \(4 \sqrt { 10 } \mathrm {~ms} ^ { - 1 }\)
Find (i) the value of \(\lambda\)
(ii) the value of \(\theta\)