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A ladder 5 m long is leaning against a wall. The bottom of the

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A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

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A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

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Text solutionVerified

Solution:

x^{2} + y^{2} = 5^{2}

\frac{d a}{d t} = + 2 c m (s)

\frac{d y}{d t} = ?

x^{2} + y^{2} = 5^{2}

w h e n x = 4 c m

y^{2} = 5^{2} - 4^{2} = 9

y = 3 c m

\frac{d ( x ^{2} + y ^{2} )}{d t} = \frac{d ( 5 ^{2} )}{d t}

\frac{d ( x ^{2} + y ^{2} )}{d t} = 0

\frac{d x ^{2}}{d t} + \frac{d y ^{2}}{d t} = 0

\frac{d x ^{2}}{d x} \frac{d x}{d t} = - \frac{d y ^{2}}{d y} \frac{d y}{d t}

2 x \frac{d x}{d t} = - 2 y \frac{d y}{d t}

= \frac{d y}{d t} y = - x 2 \frac{c m}{s}

= \frac{d y}{d t} = - \frac{x}{y} 2 \frac{c m}{s}

= - \frac{4}{3} 2 \frac{c m}{s}

= - \frac{8}{3} \frac{c m}{s}

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Question Text	A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?
Answer Type	Text solution:1
Upvotes	150

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

Text solutionVerified

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