Analysis and Approaches for IBDP Maths Ebook 2 | Page 161

2. Two cyclists A and B are at the same road intersection. A travels towards east at a
constant speed
1
40 kmh � , while B travels towards north at a constant speed
1
9 kmh � . Let
x km and y km be the distance travelled of A and B at the time t hours after they
started the journey. Let H km be the relative distance between A and B t hours after
they started the journey.
11
(a)
(b)
Show that
dH 40x � 9y
� .
dt 2 2
x � y
Hence, find the value of d H
dt
.
[4]
[3]
3. Let
z � 5.
� � . It is given that d x
�� 5 and
dt
e
2
z xy ln y
dy
e
dt �
2
. Find d z
dt
when y
� e and
[6]
4. In the figure, AC � x m , AB � 60 m , ABC ˆ
x � 60 2 and
dx
dt
�1
� 90 2 ms .
� � rad and ˆ
�
ACB � rad
6
. Find d � when
dt
[7]
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