8. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors directed due east and due north respectively and position vectors are given relative to a fixed origin.] At 7 am a ship leaves a port and moves with constant velocity. The position vector of the port is \(( - 2 \mathbf { i } + 9 \mathbf { j } ) \mathrm { km }\). At 7.36 am the ship is at the point with position vector \(( 4 \mathbf { i } + 6 \mathbf { j } ) \mathrm { km }\).

1. Show that the velocity of the ship is \(( 10 \mathbf { i } - 5 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\)
2. Find the position vector of the ship \(t\) hours after leaving port. At 8.48 am a passenger on the ship notices that a lighthouse is due east of the ship. At 9 am the same passenger notices that the lighthouse is now north east of the ship.
3. Find the position vector of the lighthouse.
4. Find the position vector of the ship when it is due south of the lighthouse.
   
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