# Math Calculus

The foot of a 30-foot ladder is being pulled away from a vertical wall at a rate of 1 foot per minute. When the top of the ladder is 6 feet from the ground, at what rate is the top of the ladder moving down the wall?

1. 👍 0
2. 👎 0
3. 👁 77
asked by Meg
1. Let the foot of the ladder be x ft from the wall, and let the top of the ladder by y ft above the ground

x^2 + y^2 = 30^2
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0

when y = 6
x^2 + 36 = 900
x = √864

given: dx/dt = 1 , x = √864 , y = 6

√864(1) + 6dy/dt = 0
dy/dt = -√864/6 ft/min or appr. -4.9 ft/min

(the negative sign shows that y is decreasing or the ladder is moving down the wall)

1. 👍 0
2. 👎 0
posted by Reiny
2. Reini - How did you ended up getting x dx/dt + y dy/dt=0?

my professor said something with
a^2 + b^2 = c^2
then differentiate it so 2a(da/dt) + 2b(db/dt) = 2c(dc/dt)

so a^2+b^2=c^2
a^2 + 6^2 = 30^2
so a=sqrt(864)

then I differentiate
let da/dt = 1
b = 6
c=30

2a(da/dt)+2b(db/dt)=2c(dc/dt)
2sqrt(864)(1)+2(6)(db/dt)=2(30)(0)
=24sqrt(6)+12db/dt = 0

but how do i sold for db/dt?

is this way correct?

thanks

1. 👍 0
2. 👎 0
posted by Meg
3. that is exactly what I did, except I used x and y instead of a and b
remember that your c is a constant, so its derivative is zero (I used the actual 30^2)

I had defined x as the distance along the ground, and we were told the base of the ladder moved out"at a rate of 1 foot per minute"
this is the same as saying dx/dt = 1

from your
24sqrt(6)+12db/dt = 0
12db/dt = -24√6
db/dt = -24√6/12 = -4.9 , the same answer as I had

so yes, you are correct

1. 👍 0
2. 👎 0
posted by Reiny
4. Thank you very much for your help :)

1. 👍 0
2. 👎 0
posted by Megan

## Similar Questions

1. ### Analytical Geometry

A 10 foot long ladder is leaning against a vertical wall with the top of the ladder 8ft from the ground. What is the slope of the ladder? How far is the foot of the ladder from the wall? Can a 6 foot tall man walk under the ladder

asked by Julius on January 4, 2015
2. ### Calculus (related rates)

A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.4 m/sec. How fast is the top sliding down the wall when the foot of the

asked by Craig on March 21, 2017
3. ### math

A ladder 10 m long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at 2 m/s. How fast is the top sliding down the wall when the foot of the ladder is 6m from the

asked by Grant on May 3, 2013
4. ### Calculus

A ladder 15 meters long leans against a vertical wall. If the foot of the ladder is being pulled away from the wall at the rate of 2 meters per minute. How fast is the top of the ladder sliding down the wall at the instant when

asked by Harra on December 4, 2016
5. ### Calculus

a 5m ladder rests against a vertical wall. The top of the ladder begins sliding down the wall at 2m/sec, while the foot of the ladder moves away from the base of the wall. How fast is the foot of the ladder moving away from the

asked by Lost One on December 21, 2012
6. ### Calculus

A 12-ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder away from the wall at the rate of 0.5ft/s. What is the configuration of the ladder at the instant that the vertical speed of the top

asked by Zoe on October 26, 2014
7. ### Calculus

related rates: a ladder, 12 feet long, is leaning against a wall. if the foot of the ladder slides away from the wall along level ground,what is the rate of change of the top of the ladder with respect to the distance of the foot

asked by JJ on January 9, 2008
8. ### math

the top of a ladder 6 m long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 m from the wall, it is sliding away from the wall @

asked by sapta on November 3, 2014
9. ### Trigonometry

The Consumer Product Safety Commission recommends that the base of a ladder should be set out 1 foot from a wall for every 4 feet of vertical rise. a. What angle will a ladder so situated make with the ground? b. If Joe follows

asked by Manuel on November 22, 2016
10. ### Maths

a ladder 25ft long leans against a wall with its foot on level ground 7ft from the base of the wall. If the foot is pulled away from the wall at the rate 2 ft/s express the distance (y) of the top of the ladder above the ground as

asked by Pia on July 8, 2013

More Similar Questions