. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1 ft/sec, and the bottom of the ladder is initially 20ft away from the wall, how fast does the ladder move up the wall 5sec after we start pushing?

0.75 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.

So we can set a Pythagoras theorem as:

Now, we need to find the derivative of above equation with respect to time.

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be:

Let us solve for y using Pythagoras theorem.

Take positive square root:

Upon substituting our given values in derivative equation, we will get:

Therefore, the ladder is moving up at a rate of 0.75 feet per second.

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step-by-step explanation: