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I need help with part C

A ship sets sail at 9 a.m. from a port P and moves with constant velocity. The position vector
of P is (4i – 8j) km. At 9.30 a.m. the ship is at the point with position vector (i – 4j) km.

(a) Find the speed of the ship in km h–1

(b) Show that the position vector r km of the ship, t hours after 9 a.m., is given by r = (4 – 6t)i + (8t – 8)j.


At 10 a.m. a passenger on the ship observes that a lighthouse L is due west of the ship.
At 10.30 a.m. the passenger observes that L is now south-west of the ship.

(c) Find the position vector of L

my working for part c

At 10am the position vector is -2i
At 10.30am the position vector is -5i+4j
Original post by 619-booyaka
I need help with part C

A ship sets sail at 9 a.m. from a port P and moves with constant velocity. The position vector
of P is (4i – 8j) km. At 9.30 a.m. the ship is at the point with position vector (i – 4j) km.

(a) Find the speed of the ship in km h–1

(b) Show that the position vector r km of the ship, t hours after 9 a.m., is given by r = (4 – 6t)i + (8t – 8)j.


At 10 a.m. a passenger on the ship observes that a lighthouse L is due west of the ship.
At 10.30 a.m. the passenger observes that L is now south-west of the ship.

(c) Find the position vector of L

my working for part c

At 10am the position vector is -2i
At 10.30am the position vector is -5i+4j


A diagram may help. What does the information at 10am tell you about one of the co-ordinates of L?

Then how can you use what you've found (the 10:30 am position) to find the other co-ordinate?

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