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 final x -components of the momenta of m1 and m2 . (d) Calculate the final y -components of the momenta of m1 and m2 . (e) Substitute the known momentum components into the general equations of momentum for the xand y -directions, along with the known mass m3, v3 cos0 and v3 sin0 , respectively, and use the identity cos0 + sin20 = 1 to obtain v3 . (g) Divide the equation for v3 sin0 by that for v3 cos0 to obtain tan0 , 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?
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 final x -components of the momenta of m1 and m2 . (d) Calculate the final y -components of the momenta of m1 and m2 . (e) Substitute the known momentum components into the general equations of momentum for the xand y -directions, along with the known mass m3, v3 cos0 and v3 sin0 , respectively, and use the identity cos0 + sin20 = 1 to obtain v3 . (g) Divide the equation for v3 sin0 by that for v3 cos0 to obtain tan0 , 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?
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