Program Explanation Given information: The projectile of mass m is shown below. Explanation: Newton’s second law of motion, F = m ⋅ a Here, F is force and m is mass and a is the acceleration and defined as d 2 x d t 2 Resolve the friction force F R in x direction and apply Newton’s second law of motion. m d 2 x d t 2 = | F R → | cos θ ........ (1) The friction force in opposite direction to the velocity v is, F R = − k v 2 The velocity is obtained as, v = ( x ′ ) 2 + ( y ′ ) 2 The value of cos θ = x ′ ( x ′ ) 2 + ( y ′ ) 2 Substitute − k v 2 for F R and x ′ ( x ′ ) 2 + ( y ′ ) 2 for cos θ in equation (1). m d 2 x d t 2 = − k v 2 x ′ ( x ′ ) 2 + ( y ′ ) 2 Substitute ( x ′ ) 2 + ( y ′ ) 2 for v in above equation, m d 2 x d t 2 = − k v 2 x ′ v m x ″ = − k v x ′ Resolve the friction force F R in y direction and apply Newton’s second law of motion

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Chapter 4.1, Problem 36P

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Program Description:Purpose of problem is to show that equation of motion of projectile are mx″=−kvx′ and my″=−kvy′−mg .

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Chapter 4.1, Problem 35P

Chapter 4.1, Problem 37P

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Chapter 4 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

Ch. 4.1 - Prob. 11P Ch. 4.1 - Prob. 12P Ch. 4.1 - Prob. 13P Ch. 4.1 - Prob. 14P Ch. 4.1 - Prob. 15P Ch. 4.1 - Prob. 16P Ch. 4.1 - Prob. 17P Ch. 4.1 - Prob. 18P Ch. 4.1 - Prob. 19P Ch. 4.1 - Prob. 20P Ch. 4.1 - Prob. 21P Ch. 4.1 - Prob. 22P Ch. 4.1 - Prob. 23P Ch. 4.1 - Prob. 24P Ch. 4.1 - Prob. 25P Ch. 4.1 - Prob. 26P Ch. 4.1 - Prob. 27P Ch. 4.1 - Prob. 28P Ch. 4.1 - Prob. 29P Ch. 4.1 - Prob. 30P Ch. 4.1 - Prob. 31P Ch. 4.1 - Prob. 32P Ch. 4.1 - Prob. 33P Ch. 4.1 - Repeat Problem 33, except with the generator...Ch. 4.1 - A particle of mass m moves in the plane with...Ch. 4.1 - Prob. 36P Ch. 4.1 - Prob. 37P Ch. 4.2 - Prob. 1P Ch. 4.2 - Prob. 2P Ch. 4.2 - Prob. 3P Ch. 4.2 - Prob. 4P Ch. 4.2 - Prob. 5P Ch. 4.2 - Prob. 6P Ch. 4.2 - Prob. 7P Ch. 4.2 - Prob. 8P Ch. 4.2 - Prob. 9P Ch. 4.2 - Prob. 10P Ch. 4.2 - Prob. 11P Ch. 4.2 - Prob. 12P Ch. 4.2 - Prob. 13P Ch. 4.2 - Prob. 14P Ch. 4.2 - Prob. 15P Ch. 4.2 - Prob. 16P Ch. 4.2 - Prob. 17P Ch. 4.2 - Prob. 18P Ch. 4.2 - Prob. 19P Ch. 4.2 - Prob. 20P Ch. 4.2 - Suppose that L1=a1D2+b1D+c1 and L2=a2D2+b2D+c2,...Ch. 4.2 - Suppose that L1x=tDx+x and that L2x=Dx+tx. Show...Ch. 4.2 - Prob. 23P Ch. 4.2 - Prob. 24P Ch. 4.2 - Prob. 25P Ch. 4.2 - Prob. 26P Ch. 4.2 - Prob. 27P Ch. 4.2 - Prob. 28P Ch. 4.2 - Prob. 29P Ch. 4.2 - Prob. 30P Ch. 4.2 - Prob. 31P Ch. 4.2 - Prob. 32P Ch. 4.2 - Prob. 33P Ch. 4.2 - Prob. 34P Ch. 4.2 - Prob. 35P Ch. 4.2 - Prob. 36P Ch. 4.2 - Prob. 37P Ch. 4.2 - Prob. 38P Ch. 4.2 - Prob. 39P Ch. 4.2 - Prob. 40P Ch. 4.2 - Prob. 41P Ch. 4.2 - Prob. 42P Ch. 4.2 - Prob. 43P Ch. 4.2 - Prob. 44P Ch. 4.2 - Prob. 45P Ch. 4.2 - Prob. 46P Ch. 4.2 - Prob. 47P Ch. 4.2 - Prob. 48P Ch. 4.3 - Prob. 1P Ch. 4.3 - Prob. 2P Ch. 4.3 - Prob. 3P Ch. 4.3 - Prob. 4P Ch. 4.3 - Prob. 5P Ch. 4.3 - Prob. 6P Ch. 4.3 - Prob. 7P Ch. 4.3 - Prob. 8P Ch. 4.3 - Prob. 9P Ch. 4.3 - Prob. 10P Ch. 4.3 - Prob. 11P Ch. 4.3 - Prob. 12P Ch. 4.3 - Prob. 13P Ch. 4.3 - Prob. 14P Ch. 4.3 - Suppose that a projectile is fired straight upward...Ch. 4.3 - Prob. 16P Ch. 4.3 - Prob. 17P Ch. 4.3 - Prob. 18P Ch. 4.3 - Prob. 19P Ch. 4.3 - Prob. 20P Ch. 4.3 - Suppose that an artillery projectile is fired from...

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Program Description: Purpose of problem is to show that equation of motion of projectile are m x ″ = − k v x ′ and m y ″ = − k v y ′ − m g .

Solution Summary: The author explains Newton's second law of motion, F=mcdot a, where F is force and m is mass.

Program Description:Purpose of problem is to show that equation of motion of projectile are mx″=−kvx′ and my″=−kvy′−mg .

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Chapter 4 Solutions