Mathematics · Oct / Nov 2021 · Paper 51 · Question 8
YMA01
As printed in the paper
The question as text
8. [In this question i and 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 (–2i + 9j) km. At 7.36 am the ship is at the point with position vector (4i + 6j) km.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
8(a)[2]
(4
+
6 )
= −
( 2
+
9 )
+
0.6
(10
i
5 )
j (
−
km h−) *
1
N.B. 1 more line of intermediate working needed and must state the answer in i
j form to earn this mark.
8(b)[2]
r
= −
( 2
i
+
9 )
j
+
t
(10
i
−
5 )
j (km) oe
r
i
j
i
j
8(c)[4]
t = 1.8:
= −
( 2
+
9 ) 1.8(10
+
−
5 )
r
=
16
i
t = 2:
r
= −
( 2
i
+
9 )
j
+
2(10
i
−
5 )
j OR
r
=
16
i
+
0.2(10
i
−
5 )
j
r
L =
19
i (km)
8(d)[4]
−+
2 10
t
=
19
2.1
t =
r
( 2
i
9 )
j
2.1(10
i
5 )
j
= −
+
+
−
r
=
(19
i
−
1.5 )
j (km)
Notes for question 8
8(a)
M1 Correct structure with t = 0.6
A1* Given answer correctly obtained
Allow verification.
8(b)
M1 Correct structure
A1 cao
M1 Correct unsimplified substitution of t = 1.8 into their r
8(c)
OR use t = 1.2 with (4
i
+
6 )
j as start point
A1 cao
M1 Correct unsimplified substitution of t = 2 into their r
OR use t = 1.4 with (4
i
+
6 )
j as start point
OR use t = 0.2 and their first answer as start point
A1 cao
8(d)
M1 Equating i component of their r to i component of their rL
A1 cao
DM1 Dependent on previous M1, for substituting their value of t into their r
A1 cao
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