Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of (Figure 1). Suppose that Matthew runs with velocity v₁ (m/s) and Jessica with velocity v (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters from P. P FIGURE 1 B Show that f(x, y) = x² + y² - 2xy cos 0. • Assume that 0 = π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 25, y = 28, va = 5 m/s, and vz = 4 m/s. df dt
Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of (Figure 1). Suppose that Matthew runs with velocity v₁ (m/s) and Jessica with velocity v (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters from P. P FIGURE 1 B Show that f(x, y) = x² + y² - 2xy cos 0. • Assume that 0 = π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 25, y = 28, va = 5 m/s, and vz = 4 m/s. df dt
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:Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0
(Figure 1).
Va
Suppose that Matthew runs with velocity va (m/s) and Jessica with velocity v (m/s).
Let f(x, y) be the distance from Matthew to Jessica when Matthew is a meters from P and Jessica is y meters
from P.
x
P
df
dt
FIGURE 1
Show that f(x,y)
√x² + y² - 2xy cos 0.
• Assume that 0 = π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and
Jessica is changing when
B
=
X =
= 25, y = 28, va = 5 m/s, and v₂ = 4 m/s.
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