(a) Explanation Given: The differential equation is as follows: d v d t = G 2 − K 2 v 2 Here, v is the velocity and t is the time. The fact is 1 G 2 − K 2 v 2 = 1 2 G [ 1 G − K v + 1 G + K v ] . Calculation: Given that, the differential equation is d v d t = G 2 − K 2 v 2 . Use the method of separation of the variable in equation d v d t = G 2 − K 2 v 2 . d v d t = G 2 − K 2 v 2 d v G 2 − K 2 v 2 = d t Use the given fact 1 G 2 − K 2 v 2 = 1 2 G [ 1 G − K v + 1 G + K v ] in the resultant equation. d v 2 G ( 1 G − K v + 1 G + K v ) = d t Now, integrate both sides as follows. ∫ d v 2 G ( 1 G − K v + 1 G + K v ) = ∫ d t 1 2 G [ ∫ ( 1 G − K v ) d v + ∫ ( 1 G + K v ) d v ] = t + c 1 2 G [ − 1 K ln ( G − K v ) + 1 K ln ( G + K v ) ] = t + c 1 2 G K ln ( G + K v G − K v ) = t + c Simplify further, ln ( G + K v G − K v ) (b) To determine The velocity as time tends to infinity and also determine the condition about the falling object in the presence of air resistance. (c) To determine The velocity of the falling cat as a function of time.

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

Author: Margaret L. Lial; Nathan P. Ritchey; Raymond N. Greenwell

Publisher: Pearson Education

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Chapter 10, Problem 74RE

(a)

To determine

The velocity as a function of time.

(b)

To determine

The velocity as time tends to infinity and also determine the condition about the falling object in the presence of air resistance.

(c)

To determine

The velocity of the falling cat as a function of time.

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Chapter 10, Problem 73RE

Chapter 11.1, Problem 1YT

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Chapter 10 Solutions

Calculus with Applications Books a la Carte Edition

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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