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Written Question #2: One day while driving your MA-2000kg car while going northe

ID: 1789670 • Letter: W

Question

Written Question #2: One day while driving your MA-2000kg car while going northeast (exactly 45° between north and east) you, very embarrassingly, smash into your instructor's MB = 1500 kg car which was going due west. The cars have a completely inelastic collision and just after the collision are going 12m/s at 30 east of north as shown. If the speed limit on this road is 30 mph = 13.4 m/s, were either of the cars speeding before the collision? For full points, your answer must include a correct numerical calculation.

Explanation / Answer

Let initial speed of car A be vA and that of car B be vB

Initial momentum of system in x direction = 2000vAcos45 - 1500vB

Initial momentum of system in y direction = 2000vAsin45

Since the collision is fully inelastic, the two cars stick after collision

Final momentum of system in x direction = 3500*12sin30=21000

Final momentum of system in y direction = 3500*12cos30 = 36373.066

From conservation of momentum,

2000vAsin45 = 36373.066

vA = 25.72 m/s(>13.4 m/s)

2000vAcos45 - 1500vB = 21000

vB = 10.25 m/s(<13.4 m/s)

Therefore, car A had exceeded speed limit