1800-150-456-789
FlagBACK
Flag Differential Calculus> A ladder,5cm long , standing on a horizon...
question mark

A ladder,5cm long , standing on a horizontal floor ,leans against a vertical wall. If the top if the ladder slides downat a rate of 10cm/s,find rate at which the angle between the floor and the ladder is decreasing when the lower end of the ladder is 2m from the wall.

Shreya Gupta , 6 Years ago
Grade
anser 3 Answers
Susmita

Last Activity: 6 Years ago

It is a right angle triangle with side adjucent to right angle x,hypotaneus l=5cm,and base length say y.
given dx/dt=10cm/s.
sinA=x/l
Or,A=sin-1(x/l)
We are asked to find out dA/dt when y=2m=200cm.
\frac{dA}{dt}=\frac{1}{\sqrt{1-\frac{x^2}{l^2}}} \frac{d(\frac{x}{l})}{dt}
        \frac{dA}{dt}=\frac{l^2}{\sqrt{l^2-x^2}} [\frac{1}{l}\frac{dx}{dt}-\frac{x}{l^2}\frac{dl}{dt}]
As l is fixed so dl/dt=0.
and y=200cm
So l2=x2+y2
Or,l2-x2=400
\frac{dA}{dt}=\frac{5}{20}*\frac{1}{5}*10
=1/2
if it helps please approve.thank u.
 

Susmita

Last Activity: 6 Years ago

Sorry.it would be
(25/20)*(1/5)*10=5/2
Forgot to do l2..................................................

Susmita

Last Activity: 6 Years ago

Oh 
y=200cm
So l2-x2=y2=(200)2
root(l2-x2)=200 and
That wont be l2.
\frac{dA}{dt}=\frac{l}{\sqrt{(l^2-x^2)}}\frac{1}{l}\frac{dx}{dt}
       =(5/200)*(1/5)*10=1/20
 
...............................................................................................................................................

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on differential calculus

question mark
the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to  move once over to level a playground. find the area of the playground in square m?
differential calculus
1 Answer Available

Last Activity: 2 Years ago

question mark
Find dy/DX when y=x^sinx+sin-1√x.
 
Please give me the solution of this problem. 
differential calculus
0 Answer Available

Last Activity: 2 Years ago

question mark
If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.
differential calculus
0 Answer Available

Last Activity: 2 Years ago

question mark
Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.
differential calculus
0 Answer Available

Last Activity: 2 Years ago

question mark
Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.
differential calculus
0 Answer Available

Last Activity: 2 Years ago