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Question

Answer 1

(5)

Step 1:

The distance between the observer and building is 24 feet.

Let the angle of elevation is .

Height of the building is .

The elevator moves up from the ground at rate 4 ft/sec.

The person moves towards building at rate 0.75 ft/sec.

Find the angle of elevation increases or decreases after 10 sec.

Now draw a triangle with the given specifications.

From the above triangle .

Apply derivative on each side with respect to t.

Step 2:

The distance between man and building after 10 sec.

The distance traveled by person after 10 sec is 7.5.

The remaining distance between the person and building is .

The position of the elevator after 10 sec.

Substitute and

0.1212 is positive and is also positive for all values of .

So is positive.

Therefore the angle of elevation increases.

Solution:

The angle of elevation increases.