7 A quad-bike, a truck and a car are moving on a large, open, horizontal surface in a desert plain. Relative to the quad-bike, which is travelling due west at its maximum speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the truck is moving on a bearing of \(340 ^ { \circ }\). Relative to the car, which is travelling due east at a speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the truck is moving on a bearing of \(300 ^ { \circ }\).

1. Show that the speed of the truck is approximately \(24.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and that it is moving on a bearing of \(318 ^ { \circ }\), correct to the nearest degree.
2. At the instant when the truck is at a distance of 400 metres from the quad-bike, the bearing of the truck from the quad-bike is \(060 ^ { \circ }\). The truck continues to move with the same velocity as in part (a). The quad-bike continues to move at a speed of \(10 \mathrm {~ms} ^ { - 1 }\). Find the bearing, to the nearest degree, on which the quad-bike should travel in order to approach the truck as closely as possible.
   [0pt] [5 marks]
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