A space probe, initially at rest, undergoes an internal

Chapter 6, Problem 6.79

(choose chapter or problem)

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m1 48.0 kg travels in the positive x- direction at 12.0 m/s, and a second piece of mass m2 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities. (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2, and v3 and the sines and cosines of the angles, taking u to be the unknown angle. (c) Calculate the fi nal x-components of the momenta of m1 and m2. (d) Calculate the fi nal y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos u and v3 sin u, respectively, and use the identity cos2 u sin2 u 1 to obtain v3. (g) Divide the equation for v3 sin u by that for v3 cos u to obtain tan u, then obtain the angle by taking the inverse tangent of both sides. (h) In general, would three such pieces necessarily have to move in the same plane? Why?