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A lamp post of length 10 meter placed at...

A lamp post of length 10 meter placed at the end A of a ladder AB of length 13 meters, 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 12 m from the vertical wall, the base B is moving at the rate of 5 m/sec. A man (M) of height 1.5 meter standing at a distance of 15 m from the vertical wall.

Rate at which `theta` decreases, when the base B is 12 m from the vertical wall, is

A

1 rad/sec

B

2 rad/sec

C

5 rad/sec

D

1/2 rad/sec

Text Solution

Verified by Experts

The correct Answer is:
A
Let WB = x at time t. Then
`x//13 = cos theta`
`therefore" "(dx)/(dt)=13(-sin theta)(d theta)/(dt)`
When WB = 12, then
`5=-13.(5)/(13).(d theta)/(dt)`
`therefore" "(d theta)/(dt)=-1 rad//s`
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