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Past exam of the mathematics course of the University of Cambridge
/
2025
/
ia
/
Paper 4
/
4B
/
Solution
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Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
2025
ia
Paper 4
4B
Created
2026-09-23
Updated
2026-09-25
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Put
R
=
R
A
+
R
B
,
c
=
R
2
−
b
2
/
R
, and
s
=
b
/
R
. At impact the unit
vector
from
A
to
B
is
n
=
(
−
c
,
s
)
. The
impulse
is normal, so tangential
velocity
is unchanged, while the normal components undergo
a
one-dimensional
elastic collision
. Therefore
v
A
=
M
A
+
M
B
2
M
B
(
u
e
x
⋅
n
)
n
=
−
M
A
+
M
B
2
M
B
u
c
n
,
(1)
v
B
=
u
e
x
−
M
A
+
M
B
2
M
A
(
u
e
x
⋅
n
)
n
=
u
e
x
+
M
A
+
M
B
2
M
A
u
c
n
.
(2)
Ancestors
(10)
4B
Paper 4
ia
2025
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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