Question

A ladder $$20$$ft long leans against a vertical wall. The top end slides downwards at the rate of $$2$$ ft per second. The rate at which the lower end moves on a horizontal floor when it is $$12$$ft from the wall is

A
83
B
65
C
32
D
174

Solution

The correct option is A $$\cfrac { 8 }{ 3 }$$since ABC is a right angled triangle $$AC^2+AB^2=BC^2\Rightarrow x^2+y^2=20^2 ..............................(1)$$ when it is 12 ft away from wall (means $$x=12$$ )$$AC^2+12^2=20^2 \Rightarrow AC = 16 \Rightarrow y=16$$Differentiating (1) w.r.t time $$t$$$$\Rightarrow 2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0$$Putting $$x=12,y=16,\dfrac{dx}{dt}=v,$$ $$\dfrac{dy}{dt}=-2('-' because \ y \ is \ decreasing )$$ we get$$\Rightarrow 2\times12\times v-2\times16\times2=0\Rightarrow v=\dfrac83$$Therefore Answer is $$A$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More