Analysis and Approaches for IBDP Maths Ebook 2 | Page 159

48
Paper 2 Section A – Rates of Change
11
Example
In the figure, OA is a vertical structure such that OA
the right with a speed of
1
5 cms � . Let OB x cm
� 10 cm . A particle B is moving to
� and AB � h cm .
When B is 7.5 cm from O ,
(a) find the rate of change of AB ;
(b) find the rate of change of ˆ OBA .
[4]
[3]
Solution
(a)
2 2 2
x �10
� h
d 2 d d 2
( x ) � (100) � ( h )
dt dt dt
(M1) for valid approach
dx
dh
2x
�0 � 2h
dt
dt
(A1) for correct approach
2 2 2
7.5 �10 � h
2
156.25 � h
h � 12.5
dh
�2(7.5)(5) � 2(12.5) A1
d t
dh
�1
� 3 cms
A1
dt
[4]
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