117. The (box)car has velocity Gvvcgi=1#relative to the ground, and the bullet has velocityGvbg022i j=+cos#sin#θθrelative to the ground before entering the car (we are neglecting the effects of gravity on the bullet). While in the car, its velocity relative to the outside ground is Gvbg082.cos##i0.8j2(due to the 20% reduction mentioned in the problem). The problem indicates that the velocity of the bullet in the car relative to the caris (with v3unspecified)Gbcj=3#. Now, Eq. 4-44 provides the condition 2231ˆˆˆˆ0.8cos i 0.8sinj jivvv+=+GGGso that equating xcomponents allows us to find θ. If one wished to find v3one could also equate the ycomponents, and from this, if the car width were given, one could find the time spent by the bullet in the car, but this information is not asked for (which is why the width is irrelevant). Therefore, examining the xcomponents in SI units leads to
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