Concept explainers
Videos
Interpretation:
The analytical solution for
Concept Introduction:
The limiting velocity of an object is called its terminal velocity. It is obtained by finding the limit of
The fixed point of the differential equation in terms of
Answer to Problem 13E
Solution:
a)
b)
c)
d)
e)
Explanation of Solution
a) The differential equation which shows the velocity
Integrating with respect to t gives
We are given that
Where
Therefore, the analytical solution for
b) The terminal velocity of the sky diver can be calculated as
Thus, the terminal velocity of the sky diver is
c) The fixed point of the
The fixed is obtained by putting
Thus, the terminal velocity of the sky diver is
d) The average velocity of the sky diver can be calculated as
e) We can find the distance fallen s from the equation for v(t) as
After substitution equation (1) becomes
But
But terminal velocity is
Therefore,
After substituting the given values we can write
After solving it we get
The drag constant k can be calculated as
Want to see more full solutions like this?
Chapter 2 Solutions
Nonlinear Dynamics and Chaos
- Write complete solution and indicate proper unitsarrow_forwardProblem 4 (10pt). Use Stokes' theorem to evaluate the line integral (zdx+xdy + ydz) where C is the triangle in the xy-plane with vertices (1,0,0), (0,1,0), and (1,2,0) with counterclockwise orientation when viewed from above.arrow_forwardProblem 3 (10pt). Let R be the portion of the plane x+y+z = 1 in the first octant (i.e, x,y,z > 0). Compute the surface integral xds.arrow_forward
- Problem 5 (10pt). Let F = xyi - zj and R is the unit square in the xy-plane, {0 < x,y≤1,z=0}. Compute curlF ds = c curlF.NdS where N is the unit upward normal vector to R.arrow_forwardProblem 6 (10pt). R Use divergence theorem to calculate the surface integral f√ F. ds = √ √ F. Nds where N is the unit outward normal vector, F = x²i – x³z²j – 4x³zk, and R is the closed surface bounded by the cylinder x² + y² = 1 and planes z = x + 2 and z = = 0.arrow_forwardProblem 2 (10pt). Let F = xyzi+yzj + zk. Compute the divergence and curl of F.arrow_forward
- The Fibbonacci sequence is defined recursevely as following for i≥3 FiFi-1+ Fi-2; F1 = 1, F2 = 1. Write a scipt that uses a for loop to compute the 10th element of the Fibbonacci sequence and assing it to the variable named farrow_forwardEN (4)(p()) 5 (3c) Prove by induction that: Vn E N using your recursive definition from (2c) for the function defined below: p = n↔ 2n(n + 1) =: N → N Begin your work on this page and continue onto pages that follow, numbered as per instructions, as needed. 0 (i) BC 0 (ii) RCS You may discuss with anyone 319arrow_forwardis this correct? my number J is 00292366, i will also provide what s and b are from the different page i got it from, if incorrect, please fix itarrow_forward
- please ignore the work already done for these as i am not sure they are correct.arrow_forward4 - het B = { [´8 ], [ -5]} and C = { [4] [1]} Find the change of coordinates. matrix from ẞ to C and from C to B.arrow_forward(5) • Let u₁ = [ ! ] 4 [ i ] = [i] = and Из These vectors are orthogonal - (you do not need to check this). Also, let y= 3452 Calculate the orthogonal projection onto span {u₁, uz, U3}. of yarrow_forward
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage