SOLUTION: The upper ending of the 13 foot-ladder leaning on vertical walling is sliding down at a constant speed of 4 ft/sec while its lower ending is moving horizontally away from the wall.

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Question 1082914: The upper ending of the 13 foot-ladder leaning on vertical walling is sliding down at a constant speed of 4 ft/sec while its lower ending is moving horizontally away from the wall. Find the speed and acceleration of the lower ending at the instant the lower ending is 5 ft from the wall.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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X%5E2%2BY%5E2=13%5E2
X%5E2%2BY%5E2=169
Differentiating,
2X%2A%28dX%2Fdt%29%2B2Y%2A%28dY%2Fdt%29=0
X%28dX%2Fdt%29=-Y%28dY%2Fdt%29
dX%2Fdt=-%28Y%2FX%29%28dY%2Fdt%29
When X=5,
5%5E2%2BY%5E2=169
Y%5E2=169-25
Y%5E2=144
Y=12
Substituting,
dX%2Fdt=-%2812%2F5%29%28-4%29
highlight%28V=dX%2Fdt=48%2F5%29ft%2Fs
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Differntiating again,
X%2A%28d2X%2Fdt2%29%2B%28dX%2Fdt%29%5E2%2BY%2A%28d2Y%2Fdt2%29%2B%28dY%2Fdt%29%5E2=0
Since the Y speed is constant the second derivative (Y wrt time) equals zero.
5%2A%28d2X%2Fdt2%29%2B%2848%2F5%29%5E2%2B12%2A%280%29%2B%285%29%5E2=0
5%2A%28d2X%2Fdt2%29=-%282304%2F25%29-25
d2X%2Fdt2=-%282304%2F125%2B5%29
highlight%28a=-%282929%2F25%29%29ft%2Fs%5E2