Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    CENGAGE ENGLISH|Exercise Subjective Type|2 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE ENGLISH|Exercise All Questions|142 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

Similar Questions

Explore conceptually related problems

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. The rate at which the length of shadow of man increases, when the base B is 12 m from vertical wall, is

If a ladder which is 10m long rests against a vertical wall. If the base of ladder slides away from the wall at 1 m/s then how fast is the top of the ladder sliding down along the wall when the base is 6 m from the wall ?

A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.

A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.

A ladder of length 5 m is placed against a smooth wall as shown in figure. The coefficient or friction is mu between ladder and ground. What is the minimum value of mu , If the ladder is not to slip?

A ladder of length 5 m is placed against a smooth wall as shown in figure. The coefficient or friction is mu between ladder and ground. What is the minimum value of mu , If the ladder is not to slip?

A ladder 5 m long leans against a vertical wall. The bottom of the ladder is 3m from the wall. If the bottom of the ladder is pulled 1 m farther from the wall, how much does the top of the ladder slide down the wall

A ladder 10 metres long rests with one end against a vertical wall, the other on the floor. The lower end moves away from the wall at the rate of 2 metres/minute. The rate at which the upper end falls when its base is 6 metres away from the wall

A ladder 5m long rests against a vertical wall. If its top slides down at the rate of 10 cm //sec , then, when the foot of the ladder is 4 m away from the wall, the angle between the floor and the ladder is decreasing at the rate of

The top of a ladder 6 metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 metres from the wall, it is sliding away from the wall at the rate of 0.5 m/sec. How fast is the top-sliding downwards at this instance? How far is the foot from the wall when it and the top are moving at the same rate?