Analysis and Approaches for IBDP Maths Ebook 2 | Page 160

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b) Let � � OBA ˆ .
10
tan� �
x
d d �10
�
(tan �)
� � �
dt dt � x �
2 d�
10 dx
sec � �� (A1) for correct approach
2
dt x dt
10
tan� �
7.5
2
� � 10 � �d�
10
� 1 � � �
� � (5)
(A1) for substitution
�
2
�7.5 � �
� �
dt
7.5
25 d� 8 ��
9 dt
9
d�
8 rads
�1
�� A1
dt
25
[3]
Exercise 48
1. In the figure, A and B are two particles such that their lines of motion are
perpendicular. The relative distance between A and B is fixed to be 50 m. A is moving
1
upward with a speed of 10 ms � . Let OB � x m and OA � y m.
When A is 14 m from O ,
(a) find the rate of change of OB ;
(b) find the rate of change of ˆ OBA .
[4]
[3]
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