An UFO of mass 4 M and zero speed is in deep space. Due to a communication probl

Question

An UFO of mass 4 M and zero speed is in deep space. Due to a communication problem between the alien crew members from different planets, the UFO explodes into three fragments when they are trying to start the engines. One fragment of mass M moves in the positive x-direction with speed 1/2V. The second fragment of mass 2M moves with speed V at an angle theta=30degree left of the positive y-axis as shown in the figure. The third fragment has mass M. Find the energy released in the explosion Simplify your expression as far as possible, using sin 30degree = 1/2, cos 30degree = 1/2 root3.

Explanation / Answer

Here,

for the velocity of third fragment V3

M * V3 + M * V/2 i + 2 M * V * (-sin(30) i + j* cos(30)) = 0

solving for V3

V3 = 0.5 V i - V j

V3 = sqrt(0.5^2 + 1^2) * V

V3 = 1.12 V

Energy released in explosion = total sum of kinetic energy

Energy released in explosion = 0.5 * 2M * V^2 + 0.5 * M * (1.12 V)^2 + 0.5 * M * (0.5 V)^2

Energy released in explosion = 1.752 M* V^2

the Energy released in explosion is 1.752 M* V^2

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