Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of theta (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) = root x^2 + y^2 - 2xy cos theta. . 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 = 22, y = 28, va = 3 m/s, and Vb = 5 m/s.
