Two automobiles of equal mass approach an intersection. One vehicle is traveling
ID: 1967403 • Letter: T
Question
Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 13.9 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 38.2° 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? What was the initial speed of the northward-moving vehicle?Explanation / Answer
let mass of each vehicle be m
let the velocity of northward-moving vehicle be vn
let the combined velocity just after collision be v
conserving momentum along east direction
m*13.9=(m+m)*v*cos(38.2o)
v=8.844 m/s
now,conserving momentun along north direction
m*vn=(m+m)*v*sin(38.2o)
vn=2*8.844*sin(38.2o) = 10.94 m/s = 63.38 mi/h which is greater than 35 mi/h so the driver of the northward-moving vehicle is not telling te truth.
the initial speed of the northward-moving vehicle is 63.38 mi/h (or) 10.94 m/s .