(a) Show that f(x, y) = Vx2 + y2 – 2xy cos 0. (b) Assume that 0 = 1/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 30, y = 20, va = 4 m/s, and v, = 3 m/s. х У B FIGURE 8
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
Jessica and Matthew are running toward the point P along the straight
paths that make a fixed angle of 0 (Figure 8). Suppose that Matthew runs
with velocity Va meters per second and Jessica with velocity Vb meters per
second. 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.
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