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1. A 5 foot ladder leaning against the wall slips up that its base moves away from the wall at 2ft/sec. How fast will the top of the ladder be moving down the wall when the base is 4ft from the wall?
2. A girl flying a kite plays out a string at 3 feet per second. The kite moves horizontally at an altitude of 100 feet. If the string is out find the rate at which the kite is moving when 260 feet of string has been played out.
3. Sand is leaking from a bag and is forming a conical pile in which the radius is 6 times as large as the height. Find the rate at which the volume is increasing when the radius is 3 inches and the height is increasing at increasing at 2 inches per minute.
1 Answer
- Anonymous10 years agoFavorite Answer
A problem at a time..
1. A 5 foot ladder leaning against the wall slips up that its base moves away from the wall at 2ft/sec. How fast will the top of the ladder be moving down the wall when the base is 4ft from the wall?
Let...
a = 4 [The base from the wall]
b = 3 [Referring to 3-4-5 Right Triangle Ratio]
c = 5 [The length of the ladder]
da/dt = 2
db/dt = ?
dc/dt = 0 [Since the length of the ladder doesn't change]
Then...
a(da/dt) + b(db/dt) = 0
Hence...
4(2) + 3(db/dt) = 0
db/dt = -8/3 ft/sec
Good luck!
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