The Xanthar mothership locks onto an enemy cruiser with its tractor beam (see the figure below); each ship is at rest in deep space with no propulsion following a devastating battle. The mothership is at $x=0$ when its tractor beams are first engaged, a distance $d=225$ xiles from the cruiser. Determine the $x$-position in xiles (measured from $x=0$ ) of the two spacecraft when the tractor beam has pulled them together. Model each spacecraft as a point particle with the mothership of mass $M=180$ xons and the cruiser of mass $m=12.0$ xons.
HINT
xiles
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Answer
The final position of the two spacecraft when they are pulled together by the tractor beam is \(\boxed{14.0625}\) xiles.
Step 1 ：Define the variables: the mass of the mothership \(M = 180\) xons, the mass of the cruiser \(m = 12.0\) xons, and the distance between the mothership and the cruiser \(d = 225\) xiles.
Step 2 ：Calculate the position of the center of mass using the formula \(x_{cm} = \frac{M*0 + m*d}{M + m}\).
Step 3 ：Substitute the given values into the formula to get \(x_{cm} = \frac{180*0 + 12.0*225}{180 + 12.0} = 14.0625\).
Step 4 ：The final position of the two spacecraft when they are pulled together by the tractor beam is \(\boxed{14.0625}\) xiles.
