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
The sum of the smallest and largest multiples of 8 up to 60 is?

If 2/3 of a number is 24 then 1/4 of a number is...

Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning:             Assume that n 2 is

Evaluate following limits. Solution: Let's begin this one off in the similar manner as the first part. Let's take the limit of each piece. This time note that since our l

The region bounded by y=e -x and the x-axis among x = 0 and x = 1 is revolved around the x-axis. Determine the volume and surface area of this solid of revolution.

what is the difference between North America''s part of the total population and Africa''s part

Savannah''s mom made a fruit smoothie that tasted so good. She put in one-fourth of a cup of diced apples, one-fifth of a cup of sliced oranges, along with half of a cup of yogurt

a circle is circumscribed about an equilateral triangle whose side is 3 cm. find the area of the circle.

The median - it is a statistical value which is usually located at the center of a given set of data that has been organized in the order of size or magnitude as illustrating,

which physics law is used to describe heat loss in cylindrical pipe