In this question \mathbf{i} is a unit vector due East and \mathbf{j} is a unit vector due North. At 12 00 hours, a ship leaves a port P and travels with a speed of 26 kmh⁻¹ in the direction 5\mathbf{i} + 12\mathbf{j}.

1. (i)Show that the velocity of the ship is (10\mathbf{i} + 24\mathbf{j}) kmh⁻¹.[2]
2. (ii)Write down the position vector of the ship, relative to P, at 16 00 hours.[1]
3. (iii)Find the position vector of the ship, relative to P, t hours after 16 00 hours.[2]
4. (iv)At 16 00 hours, a speedboat leaves a lighthouse which has position vector (120\mathbf{i} + 81\mathbf{j}) km, relative to P, to intercept the ship. The speedboat has a velocity of (-22\mathbf{i} + 30\mathbf{j}) kmh⁻¹. Find the position vector, relative to P, of the speedboat t hours after 16 00 hours.[1]
5. (v)Find the time at which the speedboat intercepts the ship and the position vector, relative to P, of the point of interception.[4]