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Unformatted text preview: WORKSHEET 19 - Fall 1995 1. In each of the following equations, suppose that each variable is actually a function of time t and differentiate each expression with respect to t . a) x 2 + y 2 = 100 b) x + s 5 = s 1 . 5 c) 40 y- xy = 80 d) ( x + 7)(7- gt 2 ) = 9 x, where g is a constant e) V = kh 3 , where k is a constant 2. While innocently painting his house from the top of a 10 foot ladder one summer day, Dr. McAdam feels a sudden jerk! Looking down he sees Nitro, the neighbor’s dog, pulling on the base of the ladder at a constant rate of 1 2 ft/sec. For the following questions assume that Dr. McAdam’s balance is very good and that the ladder was originally ﬂat against the wall! a) How far does Dr. McAdam fall during the first four seconds of motion? The next four? The next four? The next four? The last four? (Use a calculator.) b) From what you found in part a), what can you say about the rate at which Dr. McAdam is falling? c) How fast is Dr. McAdam approaching the ground when Nitro has pulled the bottom of the ladder 6 feet from the wall....
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
- Spring '08