Two automobiles traveling at right angles to each other collide and stick together. Car A has a mass of 1200 kg and had a speed of 25 m/s before the collision. Car B has a mass of 1600 kg. The skid marks show that, immediately after the collision, the wreckage was moving in a direction making an angle of 40° with the original direction of car A. What was the speed of car B before the collision?
A)16 m/s
B)18 m/s
C)11 m/s
D)21 m/s
E)14 m/s

Question

Quizplus · Accepted Answer

Explanation:Momentum is conserved in both the x and y directions.$$(1200	ext{ kg})(25	ext{ m/s})\cos0\degree+(1600	ext{ kg})(v_B)\cos90\degree=(1200	ext{ kg}+1600	ext{ kg})(v_f)\cos40\degree$$$$(1200	ext{ kg})(25	ext{ m/s})\sin0\degree+(1600	ext{ kg})(v_B)\sin90\degree=(1200	ext{ kg}+1600	ext{ kg})(v_f)\sin40\degree$$$$v_f=\frac{(1200	ext{ kg})(25	ext{ m/s})}{\cos40\degree(1200	ext{ kg}+1600	ext{ kg})}=16	ext{ m/s}$$$$v_B=\frac{(1200	ext{ kg}+1600	ext{ kg})(v_f)\sin40\degree}{\sin90\degree(1600	ext{ kg})}=16	ext{ m/s}$$

Two Automobiles Traveling at Right Angles to Each Other Collide