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 U (ft/s) 80 85 90 95 35 188 212 238 266 40 197 222| 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. f (xo + Ax, yo) –f(xo.Vo) f(xo, Yo + Ay) – f (xo. Yo) f. (xo, Yo) = lim if, (xo, yo) = lim Ax Ay-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 r with respect to v when v = 85ft/s and 0 = 45'. (b) Estimate the partial derivative of r with respect to 0 when v = 85ft/s and 0 = 45°. dr i ANGLE 0 (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 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 U (ft/s) 80 85 90 95 35 188 212 238 266 40 197 222| 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. f (xo + Ax, yo) –f(xo.Vo) f(xo, Yo + Ay) – f (xo. Yo) f. (xo, Yo) = lim if, (xo, yo) = lim Ax Ay-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 r with respect to v when v = 85ft/s and 0 = 45'. (b) Estimate the partial derivative of r with respect to 0 when v = 85ft/s and 0 = 45°. dr i ANGLE 0 (degrees)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
85
90
95
35
188
212
238
266
40
197
222 249
278
45
200 226 253
281
50
197
222
249
278
Use the accompanying table and the equations below to estimate the stated partial derivatives.
f(хо + Дх, Уо) -f (хо- Уo)
if,(xo, yo) = lim
Ay-0
f (x0, Yo + Ay) – f (xo. Yo)
Ay
f. (xo, Yo) = lim
Ax-)
Ax
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 v when v = 85ft/s and 0 = 45°.
dr
i
dv
(b) Estimate the partial derivative of r with respect to 0 when v = 85ft/s and e = 45°.
dr
ANGLE O (degrees)
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