Question

a ladder 5 meters long is leaning against a wall. the base of the ladder is sliding away from the wall at a rate of 1 meter per second. how fast is the top of the ladder sliding down the wall at the instant when the base in meters from the wall?

Answer 1

Complete question :

a ladder 5 meters long is leaning against a wall. the base of the ladder is sliding away from the wall at a rate of 1 meter per second. how fast is the top of the ladder sliding down the wall at the instant when the base is 4 meters from the wall?

Answer:

-4/3 m/s

Step-by-step explanation:

Using Pythagoras :

a² = x² + c²

5² = x² + y² - - - (1)

The horizontal distance x with respect to time t = 1m/sec

dx/dt = 1m/sec

To obtain the vertical height 'y' with respect to time t when x = 4

5² = x² + y²

Wen x = 4

5² = 4² + y²

25 = 16 + y²

y =√(25 - 16)

y = 3

Differentiate (1) with respect to t

x² + y² = 25 - ---- - (1)

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

dx/dt = 1

x = 4.

y = 3

2(4)(1) + 2(3) * dy/dt = 0

8 + 6dy/dt = 0

6 dy/dt = - 8

dy/dt = - 8/6

dy/dt = - 4/3