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isiss18
01.12.2020 •
Mathematics
Calculus Application
2. A ladder 20 feet long leans a vertical building. If the bottom of the ladder slides away from the building
horizontally at a rate of 2 ft/sec, how fast is the ladder sliding down the building when the top of the
ladder is 12 feet above the ground?
Solved
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Ответ:
-8/3 ft/s
Step-by-step explanation:We are given:
distance of the top of the ladder from the ground (h) = 12 ft
height of the ladder = 20 ft
rate of change of the distance of the base of ladder from the wall (dx/dt):
2 ft/s
Finding the distance of the base of the ladder from the wall:
From the Pythagoras's Theorem, we know that:
hypotenuse² = height² + base²
replacing the given values
20² = 12² + x²
400 = 144 + x²
x² = 256 [subtracting 144 from both sides]
x = 16 ft [taking the square root of both sides]
The rate of change of the height of the Ladder from the ground:
We know that:
h = 12 ft
(
) = ?
x = 16 ft
(
) = 2 ft/s
According to the Pythagoras's Theorem:
20² = x² + h²
differentiating both sides with respect to time
replacing the variables
Hence, the ladder will slide down at a speed of 8/3 feet per second
Ответ:
-2, 5/3
Step-by-step explanation:
It is the second one in the picture that you took