Question

exercise 6.1 question no. 10 a ladder 5m long is leaning against a wall . the bottom of the ladder is pulled along the ,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 1

Pythagoras thearom :

x^2 + y^2 = AB^2

Differentiating with T :

2x dx / dt + 2y dy / dt = 0

dx / dt = 0.02 m2^-1

x = 4 m ( given )

y = √ 5^2 - 4^2

= √ 25 - 16

= √9

= 3 .

Therefore ,

dy / dt = - x / y dx / dt

= - 4 / 3 . 0.02

= - 0.0267 ms-1