Mathematics · May / June 2024 · Paper 51 · Question 2
YMA01
As printed in the paper
The question as text
2. Two forces, P and Q, act on a particle. P has magnitude 10 N and acts due west • • Q has magnitude 8 N and acts on a bearing of 330° Given that F = P + Q, find the magnitude of F. (4) 4 5
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Show the answer and mark scheme
10
120o 8
OR
8 120o
10
Correct triangle
(
2
)
=
8
2
+
10
2
−
2
×
8
×
10 cos
θ
where θ< 180o
F
(
2
)
=
8
2
+
10
2
−
2
×
8
×
10 cos120o
F
F =
244
=
2 61
or 16 (N) or better (15.620499..)
OR:
±
(10 8cos60 )
+
o
and 8sin60o
±
Use of Pythagoras on their combined components
F =
2
(10 8cos60 )
+
o
2
+
(8sin60 )
o
2
F =
244
=
2 61
or 16 (N) or better (15.620499..)
Notes
M1: Correct triangle with lengths and the angle (arrows not needed),
2.
seen or implied.
M1:Use of cosine rule with correct structure but any angle < 180o
A1: Correct expression with or without root
A1: cao
OR:
M1: Two correct components (allow inclusion of i and j)
M1:Use of Pythagoras using their combined i cpts and j cpts
A1: Correct expression with or without root
A1: cao
N.B. A scale drawing can score Max M1M0A0A0
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