A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks

Question

A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into 2 pieces of equal mass, which fly off with velocities V1 and V2. What is the magnitude of a) V1 and b) V2? The drawing, which I will describe, depicts a rocket in the lower left corner moving diagonally in the NE direction with a dotted line. To the left of this main dotted line is where V1 is, 30 degrees to the left of it. Also, from the main dotted line is where V2 breaks off, at 60 degrees to the right of the main line. V1 looks farther away than V2, to the intersection of all 3 lines.

Explanation / Answer

I'm assuming the original was going 45 to the top of the page. (it might be different, but you can rotate). Well, we need the vertical component of the result to be 90 between the two (since momentum is conserved, and m*45=m/2*90) the horizontal components need to be the same. So in the horizontal: v1cos(30)=v2cos(60) in the vertical: v1sin(30)+v2sin(60)=90 solving the first for v in terms of x we get: v1=v2cos(60)/cos(30) v2cos(60)/cos(30)*sin(30)+v2sin(60)=90 v2=45 sqrt(3) v1=45*sqrt(3)*cos(60)/cos(30)=45

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