# Calc.

posted by .

A ladder 25ft long is leaning against the wall of a house. The ladder is pulled away from the wall at a rate of 2 ft per second. How fast is the top of the ladder moving down the wall when its base is 7ft from the wall?

• Calc. -

This is the classic problem that almost every text in Calculus uses to introduce "rate of change"

Make a diagram
Let the ladder by y ft above the ground, and
x ft away from the wall

so you have a right angled triangle
x^2 + y^2 = 25
2x dx/dt + 2y dy/dt = 0 (#1)

given : dx/dt = 2 ft/s
find : dy/dt when x = 7

when x = 7
49 + y^2 = 625
y = √576 = 24

back in #1
2(7)(2) + 2(24)dy/dt = 0
dy/dt = -28/48 = -7/12 ft/s

the negative indicates that the value of y is decreasing, or in other words, the ladder is dropping along the wall

## Similar Questions

1. ### calculus

A 20 ft ladder is leaning against the side of a house. If the bottom of the ladder is moving away from the house at the rate of 2 feet per second, how fast is the top of the ladder moving down the wall when the bottom of the ladder …
2. ### Calculus

A ladder 8 meters long is leaning against a wall. If the top of the ladder is slipping down at the rate of 8 meters per second, how fast is the bottom moving away from the wall when it is 7 meters from the wall?
3. ### mathematic

A ladder 10 meter long is leaning against a wall. If the top of the ladder is sliding down the wall at 3m/s, how fast is the angle between the top of the ladder and the wall changing when the foot of the ladder is 6 meter away from …
4. ### Calculus

a ladder 6m long is leaning against a wall. if the top of th ladder is slipping down at th rate of 13 m/s, how fast is the bottom moving away from the wall when it is 5m from the wall?
5. ### Calculus

The top of a 24 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 7 feet away from …
6. ### Calculus

A 17 foot ladder is leaning against a wall. The bottom of the ladder is moving out away from the wall at 0.6 feet per second. The top of the ladder then begins sliding down the wall. How fast is the top of the ladder going when the …
7. ### Calculas

A 13ft ladder is placed against a verticle wall. Suppose the bottom of the ladder slides away from the wall at a constant rate of 2 feet per second. How fast is the top of the ladder sliding down the wall (negitive rate) when the bottom …
8. ### Calculus

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when its base is 7 feet?
9. ### 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 the …
10. ### urgent calculus help please

A 20m long ladder is leaning against a wall. The top of the ladder is sliding down the wall at a constant speed of 2m/s. How quickly is the bottom of the ladder moving away from the wall when the bottom of the ladder is 5m from the …

More Similar Questions