A lamp post of length 10 meter placed at the end A of a ladder AB of length 13 meter, which is leaning against a vertical wall as shown in figure and its base slides away from the wall. At the instant base B is 12m from the vertical wall, the base B is moving at the rate of 5m/sec. A man (M) of height 1.5 meter standing at a distance 15m from the vertical wall, then answer the following question.
(i) Rate at which θ decreases, when the base B is 12 m from the vertical wall, is-
Text Solution
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Ans.
(i)
Sol. Let WB = x at time t, then 
= cos θ
∴ 
= 13 (– sin θ ) 
thus when WB = 12, then
5 = – 13. 
. 
i.e. 
= –1 rad/sec.
(ii)
Sol. WM = 15m
Height of the lamp post at time t = 
+ 10 m
Let λ be the length of shadow at time t, then 
= 
= 
+ 1
+ 10 = 
+ 1.5
∴ 
= 
= 
by the given condition,
we have 
+ 1= 
= 10
= 
× 
= 
= 
(iii)
Sol. tan α = 
∴ sec 2 α . 
= 
. 
= – 1.5 × 
= 
by the given condition tan α = 1.5 × 
= 0.9
∴ 
= 
cos 2 α = 
= 
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