## The variable a is the length of the ladder. The variable h is the height of the ladder’s top at time t, and x is the distance from the wall

Question

The variable a is the length of the ladder. The variable h is the height of the ladder’s top at time t, and x is the distance from the wall to the ladder’s bottom. Suppose that the length of the ladder is 6.7 meters and the top is sliding down the wall at a rate of 0.2m/s. What are the values of h and x at the moment when the top and bottom of the ladder move at the same speed? (Use decimal notation. Give your answer to three decimal places.)

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1 week 2021-09-14T23:39:55+00:00 1 Answer 0

x=4.738 meters

h=4.738 meters

Step-by-step explanation:

a = length of the ladder.

h = height of the ladder’s top at time t, and

x = distance from the wall to the ladder’s bottom.

From Pythagoras Theorem

If a=6.7 meters, then:

The top is sliding down the wall(decreasing) at a rate of 0.2m/s, therefore:

If the top and bottom of the ladder move at the same speed, then:

Taking derivative of

From

Since x=h