Home
Class 12
MATHS
If a ladder which is 10m long rests agai...

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 ?

Text Solution

Verified by Experts

Let at any instant end points of ladder is at point P(a,0) and Q(0,b) .
Length of ladder = 10 hence `a^(2)+b^(2)=100`
Differentiate w.r.t.
`2a""(da)/(dt)+2b""(db)/(dt)=0`
Given that , `(da)/(dt)=` 1m/s when a=6m, b=8 m
` 6xx 1+8""(db)/(dt)=0`
`(db)/(dt)=-(3)/(4)` m/s
So, top of the ladder will be sliding down at a rate of `(3)/(4) m//s ` .
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise TRY YOURSELF|39 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise Assignment SECTION-A (Competition Level Questions)|50 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

A ladder 10m long rests against a vertical wall. If the foot of the ladder is 6m away from the wall and the ladder just reaches the top of the wall, how high is the wall?

A ladder 10 meter long is leaning against a vertical wall. If the bottom of the ladder is pulled horizontally away from the wall at the rate of 1.2 meters per seconds, find how fast the top of the ladder is sliding down the wall when the bottom is 6 meters away from the wall

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 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/s, then the rate (in cm/s) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is

A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25cm//sec., then the rate ("in cm"//"sec".) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is :

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

A 13-m long ladder is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 m/s. How fast is its height on the wall decreasing when the foot of the ladder is 5m aways from the wall ?

A ladder 5m long is leaning against a wall. The bottom of the ladder is pulled along the ground,away from the wall,at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall?

A ladder 5m long is leaning against a wall. The bottom of the ladder is pulled along the ground,away from the wall,at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall?

A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 1.5m/sec. The length of the highest point of the ladder when the foot of the ladder 4.0 m away from the wall decreases at the rate of