Two automobiles of equal mass approach an intersection. One vehicle is traveling
ID: 778669 • Letter: T
Question
Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 12.5 m/s toward the east and the other is traveling north with speed v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 56.0° north of east. Determine the initial speed v2i of the northward-moving vehicle.
m/s
The speed limit for both roads is 35 mi/h and the driver of the northward-moving vehicle claims he was within the speed limit when the collision occurred. Is he telling the truth?
Yes No
Explanation / Answer
a)
let East be +x axis
let V is the final speed of both vehicles.
Apply conservation of momentum in x-direction
m*12.5 + 0 = (m + m)*V*cos(56)
V*cos(56) = 6.25 ----(1)
Apply conservation of momentum in y-direction
0 + m*v2i = (m + m)*V*sin(56)
V*sin(56) = V2i/2 -----(2)
take equation(2)/equation(1)
tan(56) = (V2i/2)/6.25
v2i = 12.5*tan(56)
= 18.5 m/s <<<<<<<<<-------------------Answer
b) Yes. He is telling the truth.