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M1 June 2011 Q7 Vectors Question watch

1. I don't understand the logic for part d at all. I'd appreciate the help

[In this question, i and j are horizontal unit vectors due east and due north respectively
and position vectors are given with respect to a fixed origin.]
A ship S is moving along a straight line with constant velocity. At time t hours the position
vector of S is s km. When t = 0, s = 9i – 6j. When t = 4, s = 21i + 10j. Find
(a) the speed of S,

(b) the direction in which S is moving, giving your answer as a bearing.

(c) Show that s = (3t + 9) i + (4t – 6) j.

A lighthouse L is located at the point with position vector (18i + 6j) km. When t = T, the
ship S is 10 km from L.
(d) Find the possible values of T.
2. (Original post by salihahmehmood)
I don't understand the logic for part d at all. I'd appreciate the help

[In this question, i and j are horizontal unit vectors due east and due north respectively
and position vectors are given with respect to a fixed origin.]
A ship S is moving along a straight line with constant velocity. At time t hours the position
vector of S is s km. When t = 0, s = 9i – 6j. When t = 4, s = 21i + 10j. Find
(a) the speed of S,

(b) the direction in which S is moving, giving your answer as a bearing.

(c) Show that s = (3t + 9) i + (4t – 6) j.

A lighthouse L is located at the point with position vector (18i + 6j) km. When t = T, the
ship S is 10 km from L.
(d) Find the possible values of T.
I will write the vectors as column vectors as I think it is easier to see what is going on.
From part c we have

.
This is the vector equation of the line. We are trying to find when S is 10 away from the position vector
.
Notice how 10km is 2 times the magnitude of the direction vector of the path of S?
What can you deduce from that?
3. (Original post by salihahmehmood)
I don't understand the logic for part d at all. I'd appreciate the help

[In this question, i and j are horizontal unit vectors due east and due north respectively
and position vectors are given with respect to a fixed origin.]
A ship S is moving along a straight line with constant velocity. At time t hours the position
vector of S is s km. When t = 0, s = 9i – 6j. When t = 4, s = 21i + 10j. Find
(a) the speed of S,

(b) the direction in which S is moving, giving your answer as a bearing.

(c) Show that s = (3t + 9) i + (4t – 6) j.

A lighthouse L is located at the point with position vector (18i + 6j) km. When t = T, the
ship S is 10 km from L.
(d) Find the possible values of T.
http://www.thestudentroom.co.uk/forumdisplay.php?f=38
4. (Original post by B_9710)
I will write the vectors as column vectors as I think it is easier to see what is going on.
From part c we have

.
This is the vector equation of the line. We are trying to find when S is 10 away from the position vector
.
Notice how 10km is 2 times the magnitude of the direction vector of the path of S?
What can you deduce from that?
5. (Original post by B_9710)
I will write the vectors as column vectors as I think it is easier to see what is going on.
From part c we have

.
This is the vector equation of the line. We are trying to find when S is 10 away from the position vector
.
Notice how 10km is 2 times the magnitude of the direction vector of the path of S?
What can you deduce from that?
That it's 2(3i + 4j)?

Posted from TSR Mobile
6. (Original post by salihahmehmood)
That it's 2(3i + 4j)?

Posted from TSR Mobile
Right. also notice that the path of S takes it to the position of the lighthouse. So 10km from the lighthouse is 2 direction vectors from the lighthouse.

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