Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range rof the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 85 188 212 75 80 90 35 165 238 197 222 249 40 173 45 176 200 226 253 50 173 197 222 249 Use the accompanying table and the equations below to estimate the partial derivatives. f (xo + Ax, yo) – f (xo, yo) f (xo. yo + Ay) – f (xo. yo) (xo. Yo) = lim ,(xo. Yo) = lim- Ar 4y-0 Ay Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of rwith respect to v when v = 80ft/s and 0 = 40°. dr (b) Estimate the partial derivative of rwith respect to 0 when v = 80ft/s and 0 = 40°. dr ANGLE O (degrees)
Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range rof the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 85 188 212 75 80 90 35 165 238 197 222 249 40 173 45 176 200 226 253 50 173 197 222 249 Use the accompanying table and the equations below to estimate the partial derivatives. f (xo + Ax, yo) – f (xo, yo) f (xo. yo + Ay) – f (xo. yo) (xo. Yo) = lim ,(xo. Yo) = lim- Ar 4y-0 Ay Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. (a) Estimate the partial derivative of rwith respect to v when v = 80ft/s and 0 = 40°. dr (b) Estimate the partial derivative of rwith respect to 0 when v = 80ft/s and 0 = 40°. dr ANGLE O (degrees)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by
Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves
Nolan's hand and the angle 0 above the horizontal at which it is thrown.
SPEED v (ft/s)
80
90
188 212
75
85
35
165
238
40
173
197
222
249
45
176
200
226
253
50
173
197
222
249
Use the accompanying table and the equations below to estimate the partial derivatives.
f (xo + Ar, yo) - f (xo- yo)
f.(Xo, Yo) = lim
Ax-0
f (xo. yo + Ay) – f (xo, yo)
= lim
Ay-0
Ax
Ay
Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer.
(a) Estimate the partial derivative of r with respect to vwhen v = 80ft/s and 0 = 40°.
dv
(b) Estimate the partial derivative of r with respect to 0 when v = 80ft/s and 0 = 40°.
dr
i
ANGLE O (degrees)
18
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
