Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of θ (Figure 1). Suppose that Matthew runs with velocity va (m/s) and Jessica with velocity vb (m/s). Let f(x,y) be the distance from Matthew to Jessica when Matthew is x meters from P and Jessica is y meters from P.

Question

Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of θ (Figure 1). Suppose that Matthew runs with velocity va (m/s) and Jessica with velocity vb (m/s). Let f(x,y) be the distance from Matthew to Jessica when Matthew is x meters from P and Jessica is y meters from P.
Show that f(x,y)=sqrt(x^2+y^2−2xycosθ). Assume that θ=π/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when 
x=23, y=25, va=5 m/s, and vb=2 m/s.
df/dt=

y44 · Answer

tewt