Answer: 8.6 m/s
Explanation:
Assuming no external forces present during the collision, total momentum must be conserved.
As momentum is a vector, if we decompose it in two perpendicular components (one N-S and the other W-E), total momentum must be conserved for both directions.
Prior to collision, the only component in the eastbound direction was due to the Volkswagen:
px = mvolk. Vvolk = 1,200 kg. Vvolk
After the collision, we have a component along this axis, which is the projection of the momentum vector due to both cars stuck together, 35º north of the east:
pxf = (mvolk + mcad) . vf . cos 35º (1)
With this same reasoning, we can write the following equation for the momentum on the N-S axis:
py1 = 1,800 kg. 4.0 m/s = (1,800 + 1,200) kg. Vf. sin 35º (2)
Dividing both sides in (2) and (1), we get:
1,800. 4.0 / 1,200. Vvolk = tg 35º
Solving for Vvolk:
Vvolk= 7,200 / 1,200. tg 35º = 8.6 m/s
