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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 5 foot ladder is leaning against a 4 foot wall how far must the bottom of the ladder be from the base of the wall so that the top of the ladder rests on the top of the wall?
1 i think other people feel free to change this
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
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
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 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
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.
A ladder is leaning against a building so that the distance from the ground to the top of the ladder is one foot less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 5 feet?
A. 11 feet B. 13 C. 12 D. 14.
When A 12 foot extension ladder is placed against a wall To achieve the proper climbing angle approximately how far should the bottom of the ladder be from the base of the wall?
3 FEET
