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
5 meters
13
12 feet.
1 i think other people feel free to change this
Use Pythagoras' theorem: 152-92 = 144 and the square root of 144 is 12 Answer: 12 feet
56
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.
9.2
5 meters
5 meters
The pencil was vertical to the ladder.
12
13
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.
12 feet.
A. 11 feet B. 13 C. 12 D. 14.
3 FEET