9. A spent fuel tank in space is moving in the +x direction with a speed v. It t
ID: 1779926 • Letter: 9
Question
9. A spent fuel tank in space is moving in the +x direction with a speed v. It then explodes into three picces. Just after the explosion, one piece, of mass 2m, moves with velocity v in the positive x-direction, and a second piece, with mass m, moves with a velocity v, at an angle of 60 (up or ty axis) with respect to the +x axis. The third piece with mass m moves with velocity v at an angle (down or -y axis) of 30° with respect to the +x axis. Assume no mass is lost in the explosion. what is the magnitude of the velocity v, in terms of v Just after the explosion (8 points)? (a) V.Explanation / Answer
Applying momentum conservation,
4 m v i = (2 m vi ) + ( m v1 (cos60i + sin60j)) + (m v2)
v2 = (2 v - 0.5 v1 )i - v1 sin60 j
and tan(30) = v1 sin60 / 2v - 0.5v1
1.155v - 0.289 v1 = 0866 v1
v1 = v
v2 = 1.5vi - 0.866v j
Energy addedd = Kf - Ki
= 2m v^2 /2 + m v^2 /2 + m (1.5^2 + 0.866^2)v^2 /2 - 4 m v^2 / 2
= 6 m v^2 /2 - 4 m v^2 / 2
= m v^2
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