A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece o

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A Space Probe Initially At Rest Undergoes An Internal Mechanical Malfunction And Breaks Into Three Pieces One Piece O 1 (71.38 KiB) Viewed 67 times

A Space Probe Initially At Rest Undergoes An Internal Mechanical Malfunction And Breaks Into Three Pieces One Piece O 2 (55.22 KiB) Viewed 67 times

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m₁ = 49.0 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 16.4 m/s. The third piece has mass m3 = 112 kg. (Assume that the +x-axis is to the right and the +y-axis is up along the page.) (a) Sketch a diagram of the situation, labeling the different masses and their velocities. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (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 to be the unknown angle. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (c) Calculate the final x-components of the momenta of m₁ and m₂. (Indicate the direction with the sign of your answer.) m₁ Px1= kg m/s m₂: Px2= kg m/s (d) Calculate the final y-components of the momenta of m₁ and m₂. (Indicate the direction with the sign of your answer.) m₁: Py1 kg m/s m₂ kg m/s 1= Py2 = (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet.
(f) Solve the two momentum equations for v3 cos and v3 sin 0, respectively, and use the identity cos² 0 + sin² 0 = 1 to obtain v3. V3 m/s = (g) Divide the equation for v3 sin by that for V3 cos to obtain tan 0, then obtain the angle by taking the inverse tangent of both sides. ° counterclockwise from the +x-axis 0 = (h) In general, would three such pieces necessarily have to move in the same plane? Why?