Graphical understanding of derivatives, Mathematics

Graphical Understanding of Derivatives:

A ladder 26 feet long is leaning against a wall. The ladder begins to move such that the bottom end moves away from the wall at a constant velocity of 2 feet by per second.   What is the downward velocity of the top end of the ladder when the bottom end is 10 feet from the wall?

Solution:

Begin with the Pythagorean Theorem for a right triangle:     a2 = c2 - b2

Obtain the derivative of both sides of this equation with respect to time t.  The c, representing the length of the ladder is a constant.

2a(da/dt) = -2b(db/dt)

a(da/dt) = -b (db/dt)

But, db/dt is the velocity at that the bottom end of the ladder is moving  away  from  the  wall,  equal  to  2  ft/s,  and  da/dt  is  the downward  velocity  of the top end of the ladder  along  the wall, that is the quantity  to be determined.  Set b equal to 10 feet, substitute the known values into the equation, and solve for a.

a2 = c2 - b2

 

2442_Graphical Understanding of Derivatives.png

a= 24 ft

a(da/dt) = -b (db/dt)

(da/dt) = -b/a (db/dt)

(da/dt) = -10 ft/24 ft(2 ft/s)

(da/dt) = -0.833 ft/s

Therefore, when the bottom of the ladder is 10 feet from the wall and moving at 2ft/sec., the top of the ladder is moving downward at 0.833 ft/s. (The negative sign denotes the downward direction.)

Posted Date: 2/11/2013 1:04:24 AM | Location : United States







Related Discussions:- Graphical understanding of derivatives, Assignment Help, Ask Question on Graphical understanding of derivatives, Get Answer, Expert's Help, Graphical understanding of derivatives Discussions

Write discussion on Graphical understanding of derivatives
Your posts are moderated
Related Questions
Tabulated values of the dynamic and kinematic viscosity of aqueous sodium chloride solutions have been researched in the academic literature (Kestin et al 1981). The data availab

How do you simplify 10:30:45

1. Let , where  are independent identically distributed random variables according to an exponential distribution with parameter μ. N is a Binomially distribut

The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?

theory about solving sequencing problem using graphical method

the ratio of boys to girls in the sixth grade is 2:3 if there are 24 boys, how many are girls?

i have problems with math and my teacher said that i am still progressing in math


tom has 150 feet of fencing to enclose a rectangular garden. if the length is to be 5 feet less than three the width, find the area of the garden

Equation for the given intervaks in the intervaks, giving ypout answer correct to 0.1 1.sin x = 0.8 0 2. cos x =-0.3 -180 3.4cos theta- cos theta=2 0 4. 10tan theta+3=0 0