The jet stream is flowing due east at velocity \(v_{J}\) relative to the ground. An aircraft is traveling at velocity \(v_{C}\) in the northeast direction relative to the air.

(a) Relative to the ground, find the speed of the aircraft and the angle of its motion relative to the east.

(b) Keeping the same speed \(v_{C}\) relative to the air, at what angle would the plane have to move through the air relative to the east so that it would travel northeast relative to the ground?