CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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
loader
B
65
loader
C
32
loader
D
174
loader

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 $$A$$

812213_876671_ans_c4cbf3d2ed40401a9fafc0575e77359f.png

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image