(INTERPRETATION) interpret this problem with solution

Question

INTERPRET THIS PROBLEM with solution

A 8-meter ladder is leaning against a house on flat ground. The house is to the left of the ladder. The base of the ladder starts to slide away from the house. When the base has slid to 4 meters from the house, it is moving horizontally at the rate of 1.5m/s. How fast is the ladder's top sliding down the wall when the base is 4 meters from the house?

Answer 1

So in this system, the ladder forms a right triangle with hypotenuse length of 8m. The base and height of this right triangle, denoted by b and h, have the relationship b² + h² = 8², because of the Pythagorean theorem.

We apply implicit differentiation on both sides to get 2b·b' + 2h·h' = 0, where b' is the rate of change of the base, and h' is the rate of change of the height.

We know that the base is 4 m, therefore the height must be 4√3 m. we also know that b' = 1.5 m/s. We can just plug everything in and solve for h'.

2(4)(1.5)+2(4√3)·h' = 0

Solving for h' should give you –0.867 m/s. Which means that the ladder is going 0.867 m/s in a downward direction.

Answer 2

b=4

b' = 1.5

h = 8

h'= 0

a = sqr(8^2 -4^2) = sqr (64-16) = sqr48=4sqr3

use the pythagorean thereom

h^2 = a^2 + b^2

2hh'=2aa'+2bb'

hh'=aa'+bb'

8(0) = sqr48(a') +4(1.5)

0 = a'sqr48 + 6

a' = -6/sqr48

= -6sqr48/48

= -6(4)sqr3/48 =

=-24sqr3/48

=-sqr3/2

= about -1.732/2

= about -.866 meters per second