Graphical understanding of derivatives, Mathematics

Assignment Help:

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.)


Related Discussions:- Graphical understanding of derivatives

Multiple integrals, how to convert double integral into polar coordinates a...

how to convert double integral into polar coordinates and change the limits of integration

What is conditional probability, Q. What is Conditional Probability? A...

Q. What is Conditional Probability? Ans. What is the probability that George will pass his math test if he studies? We can assume that the probabilities of George passing

Differential equation and laplace transform, 1. Solve the given differentia...

1. Solve the given differential equation, subject to the initial conditions: . x2y''-3xy'+4y = 0 . y(1) = 5, y'(1) = 3 2. Find two linearly independent power series soluti

Trignometry, Define the given satatement : 1.sin90-sin89=sin10 using pythag...

Define the given satatement : 1.sin90-sin89=sin10 using pythagoras theoram 2. How can any value of sin and cosis always given any value of cosec.

Graphing formulas, how do you graph y+3=-x+3x on a TI-83 graphing calculato...

how do you graph y+3=-x+3x on a TI-83 graphing calculator?

Example of business applications, An apartment complex contains 250 apartme...

An apartment complex contains 250 apartments to rent.  If they rent x apartments then their monthly profit is specified by, in dollars,,                                      P ( x

Illustration of rank correlation coefficient, Illustration of Rank Correlat...

Illustration of Rank Correlation Coefficient Sometimes numerical data such refers to the quantifiable variables may be described after which a rank correlation coefficient may

Maths, what is the diameter of a circle

what is the diameter of a circle

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd