0
If h is vertical height, b=horizontal distance from wall to bottom of ladder and l=lenght of ladder,we can say lsquared = hsquared + b squared.
Now differentiate w.r.t. time t.
2l*dl/dt= 2h* dh/dt + 2b*db/dt =0
However this solution doesn't give exactly the same answer when one solves the problem geometrically or using simple pythagorus.
For example ,if l=20m and b=12 m and h=16m and db/dt is 2m/s, I calculate dh/dt as !.5 m/s using calculus but 1.717 m/s using geometry or straight Pythagorus. Where is the fallasy inthe method using calculus?
Ray Bevan
What else can I help you with?
A painter is standing at the base of a ladder that is leaning against the side of a house. What angle do the ladder and the house form?
The angle formed between the ladder and the house is typically a right angle (90 degrees) if the ladder is resting against the wall of the house. This assumes that the base of the ladder is on the ground and the wall is vertical. If the ladder is leaning at an angle, the specific angle would depend on how far the base of the ladder is from the wall and its height against the wall.
A 10 meter ladder is leaning against a building. The bottom of the ladder is 5 meters from the building. How many meters high is the top of the ladder?
5 meters
A 10 foot ladder is leaning against a vertical wall the base of the ladder is 3 feet from the wall how high is the point where the ladder touches the wall?
13
A 15 foot ladder is leaning against a 30 foot wallthe bottom end of the ladder is 9 feet from the wallhow many feet above the ground does the ladder touch the wall?
12 feet.
A ladder of length L moves with its ends in contact with a vertical wall and a horizontal floor If the ladder starts from a vertical position and its lower end A moves along the floor with a constant?
As the ladder moves with its lower end along the floor at a constant speed, the top end of the ladder slides down the wall. The relationship between the height of the ladder on the wall and the distance from the wall to the bottom of the ladder can be described by the Pythagorean theorem, where (x^2 + y^2 = L^2) (with (x) as the horizontal distance and (y) as the height on the wall). As the bottom moves outward, the height decreases, illustrating a dynamic relationship governed by the constraints of the ladder's length. This setup creates a classic example of related rates in calculus, where the rate of change of the height of the ladder on the wall is influenced by the rate of change of its position on the floor.
A 24-foot ladder is placed against a vertical wall of a building with the bottom of the ladder standing on level ground 22 feet from the basse of the building?
56
A 10-m ladder is leaning against a building The bottom of the ladder is 5 m from the building. how high is the top of the ladder?
Its pythagoras: 102 - 52 = vertical height2. So 100-25 = vertical height2. Then the square root of 75 must = vertical height. Which makes the top of the ladder 8.66 feet (8ft 8 inches) from the ground.
A 10-foot ladder is leaning against a tree The bottom of the ladder is 4 feet away from the bottom of the tree About how high up the tree does the top of the ladder reach?
9.2
What are the stiles on a ladder?
The stiles on a ladder are the vertical side rails that provide support and structure. They run from the top to the bottom of the ladder, connecting the rungs, which are the horizontal steps. Stiles are essential for the ladder's stability and strength, ensuring safe use when climbing.
A painter is standing at the base of a ladder that is leaning against the side of a house. What angle do the ladder and the house form?
The angle formed between the ladder and the house is typically a right angle (90 degrees) if the ladder is resting against the wall of the house. This assumes that the base of the ladder is on the ground and the wall is vertical. If the ladder is leaning at an angle, the specific angle would depend on how far the base of the ladder is from the wall and its height against the wall.
A 10 meter ladder is leaning against a building The bottom of the ladder is 5 meters from the building How many meters high is the top of the ladder?
5 meters
A 10 meter ladder is leaning against a building. The bottom of the ladder is 5 meters from the building. How many meters high is the top of the ladder?
5 meters
A 15-foot ladder is leaning against a 30-foot wall The bottom end of the ladder is 9 feet from the wall How many feet above the ground does the ladder touch the wall?
12
A 10 foot ladder is leaning against a vertical wall the base of the ladder is 3 feet from the wall how high is the point where the ladder touches the wall?
13
Can you give me a sentence using the word vertical?
The pencil was vertical to the ladder.
A 15 foot ladder is leaning against a 30 foot wallthe bottom end of the ladder is 9 feet from the wallhow many feet above the ground does the ladder touch the wall?
12 feet.
Why is a ladder considered an inclined plane?
A ladder can be considered an inclined plane because it forms a sloping surface that allows for easier vertical movement. By leaning the ladder against a wall or structure, it creates an angle which reduces the effort required to climb compared to climbing straight up. Just like an inclined plane, a ladder allows someone to use less force to overcome the vertical height.
