Question

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m₁ = 46.6 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 16.0 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.

(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 θ to be the unknown angle.

(c) Calculate the final x-components of the momenta of m₁ and m₂. (Indicate the direction with the sign of your answer.)

(d) Calculate the final y-components of the momenta of m₁ and m₂. (Indicate the direction with the sign of your answer.)

(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 θ and v₃ sin θ, respectively, and use the identity cos²θ + sin²θ = 1 to obtain v₃.

v₃₌

(g) Divide the equation for v₃ sin θ by that for v₃ cos θ to obtain tan θ, then obtain the angle by taking the inverse tangent of both sides.

θ =  ° counterclockwise from the +x-axis

(h) In general, would three such pieces necessarily have to move in the same plane? Why?

Answer 1