# Exam 1 - MATH 1014.03MW Exam 1 Monday, January, 24 2000...

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MATH 1014.03MW Exam 1 Monday, January, 24 2000 NAME: Student Number: No. Marks Instructions : This exam contains 4 questions and has a total of 100 marks. Show all of your work. (30 Marks)A 5 meters long ladder is leaning against a building. The bottom of the ladder is dragged along the ground, away from the building, at 3 meters per minute. How fast is the top of the ladder moving down the side of the building when it is 3 meters above the ground? Solution ( i ). We draw the following figure. ( ii ). Hypotheses: x '( t )=3, | AB |=5 and . ( iii ). Question: Find y '( t ) when y ( t )=3. ( Method 1 ) By the above figure, we have Taking the derivative of Eq. relative to t , we have This implies

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By Eq. , we have . This, together with Eq. , implies When x '( t )=3 and y ( t )=3, we have . ( Method 2 ) By the above figure, we have This implies Taking the derivative of Eq. relative to t , we have By Eq. , we have . This, together with Eq. , implies When x '( t )=3 and y ( t )=3, we have . ( Method 3
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## This note was uploaded on 12/16/2009 for the course MATH 1014 taught by Professor Ganong during the Fall '09 term at York University.

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Exam 1 - MATH 1014.03MW Exam 1 Monday, January, 24 2000...

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