An isolated mass of 7.0 kg is at rest. Then it suddenly explodes into three piec

Question

An isolated mass of 7.0 kg is at rest. Then it suddenly explodes into three pieces. Piece A (mass 2 kg) moves directly leftward along the x-axis at a speed of 5 m/s. Piece B (mass 4 kg) moves at a speed of 7 m/s at an angle 40 degrees above the +x-axis. The third piece has a mass of 1 kg. A) Determine the speed of the third piece. B) Determine the direction of travel of the third piece as an angle relative to the +x-axis. C) Determine the total kinetic energy generated in this explosion.

Explanation / Answer

By conservation of momentum along x-axis: (2*5) + (4*Vb*cos40) + (1*Vcx) = 0 => Vcx = ..... ........... By conservation of momentum along y-axis: (2*0) + (4 * Vb * sin40) + (1*Vcy) = 0. ............ Now we have two linear equation and two variables (Vcx and Vcy). Thus solve for it in terms of Vb. Thus, angle = atan(Vcy/Vcx). K.E. = 0.5*[2*5^2 + 4*Vb^2 + 1*{Vcx^2 + Vcy^2}^0.5]

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