Two automobiles of equal mass approach an intersection. One vehicle is traveling
ID: 2058811 • Letter: T
Question
Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 12.3 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 57.6° 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 us take the final velocity into 2 components
taking horizontal(west to east) component only
by conservation of momentum
m(12.3+ 0 ) = 2m(Vh) (since they stick their masses will be m+m)
=>Vh = 6.15m/s
vertical component is Vy
Vy/Vh = tan(57.6) = 1.57
=> Vy = 9.655
conserving momentum along vertical direction
=> m(v2) = 2m(9.655)
=> v2 = 19.31m/s = 43.2mile/hr
the driver is quite obviously not honest