Question

(1 point) Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0 (Figure 1). Suppose that Matthew runs with velocity va (m/s) and Jessica with velocity v (m/s). Let f(t, y) be the distance from Matthew to Jessica when Matthew is z meters from Pand Jessica is y meters from P. P V B FIGURE 1 Show that f(x,y) x2 + y2 – 2xy cos. • Assume that 0= /3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 25, y = 16, V = 4 m/s, and vp = 3 m/s. df dt

Answer 1

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Answer 2

Show that $f(x,y)=\sqrt{x^2+y^2-2xy\cos \theta }$. 

$\bullet$ Assume that $\theta =\pi /3$. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when 

$x=18$, $y=21$, $v_a=5\mathrm{m}/\mathrm{s}$, and $v_b=2\mathrm{m}/\mathrm{s}$.