Ladder From
Posted on April 11th, 2009 by admin
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Ladder From
ladder sliding down the wall at the instant when the base of the ladder is 21 feet from the wall?
The base of a 35 ft ladder is being pulled away from a wall at a rate of 6 feet per second. How fast is the top of the ladder sliding down the wall at the instant when the base of the ladder is 21 feet from the wall?
Ok use pythagorean theorem equation
x^2 + y^2 = 35^2
In the instant when x is 21 ft from wall we can find that the height of the ladder (y) is 28 ft. Now take the time derivative of the pythagorean equation.
2x*dx/dt + 2y*dy/dt = 0
x*dx/dt = y*dy/dt
dy/dt = (x/y)*dx/dt = (21/28)*(6)
dy/dt = 4.5 ft/sec
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Rush - Jacob's Ladder (Live)
Related rates, how fast will the ladder be moving away from the wall when the top is 11 feet above the ground?
A 16 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how fast will the foot of the ladder be moving away from the wall when the top is 11 feet above the ground?
Let:
x be the distance of the foot of the ladder from the wall,
y be the height up the wall of the top of the ladder.
Then:
x^2 + y^2 = 16^2 ft^2 ...(1)
Differentiating with respect to x:
2x + 2y (dy/dx) = 0
dy/dx = - x / y
Therefore:
(dy/dt) / (dx/dt) = - x / y
dx / dt = - (y / x)(dy / dt) ...(2)
From (1):
When y = 11ft, x = sqrt(135) ft.
Substituting these values in (2):
dx / dt = - [ 11 / sqrt(135) ](- 2)
= 1.89 ft/s to 3 sig. fig.
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Indeed 2 fireman were reported to have minor injuries when a ladder from one of the trucks collapsed. Could have been a VERY bad deal, but thankfully everyone treated was released with no serious injuries.
Our town has lost a really neat building, several business owners have lost their businesses, and several people have lost their homes. THANKFULLY noone lost their lives. I just hope everybody had enough insurance to move on comfortably.
I cackled out loud at ya'll walking into a brown cafe and everyone stopping, turning and staring – welcome to ex-patriotism, I guess! (Crazy Americans.) I suspected they were reformulating Heineken for Americans – I just couldn't imagine the Dutch would have *such* terrible taste in beer! (Again: crazy Americans.) Hey, if you're climbing down a ladder from a tiny 'Dam apartment, does that mean you're basically Anne Frank now?
Thanks for the update – love you and miss you both! L