Two automobiles of equal mass approach an intersection. One vehicle is traveling
ID: 1969466 • Letter: T
Question
Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 14.1 m/s toward the east, and the other is traveling north with velocity v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 53.5° north of east. The speed limit for both roads is 35 mi/h, and the driver of the northward-moving vehicle claims he was within the limit when the collision occurred. Is he telling the truth?Explanation / Answer
vehicle 1 's velocity = (14.1)i m/s
vehicle 2's velocity = (v2i)j m/s
after collision
velocity of stuck vehicle system = v m/s 53.5 degrees north of east
= (vcos53.5)i + (vsin53.5)j m/s
applying momentum conservation :
14.1 X m = vcos53.5 X 2m
v = 11.85 m/s
(v2i) X m = vsin53.5 X 2m
v2i = 1.61 X v = 19.05 m/s
and limit is 35 mi/h = 56.315 km/h = 15.64 m/s
so v2i is above limit .
No, he was lying