For the Texas Department of Public Safety, you are investigating an accident tha
ID: 1438381 • Letter: F
Question
For the Texas Department of Public Safety, you are investigating an accident that occurred early on a foggy morning in a remote section of the Texas Panhandle. A 2012 Prius traveling due north collided in a highway intersection with a 2013 Dodge Durango that was traveling due east. After the collision, the wreckage of the two vehicles was locked together and skidded across the level ground until it struck a tree. You measure that the tree is 35 ft from the point of impact. The line from the point of impact to the tree is in a direction 39 north of east. From experience, you estimate that the coefficient of kinetic friction between the ground and the wreckage is 0.45. Shortly before the collision, a highway patrolman with a radar gun measured the speed of the Prius to be 50 mph and, according to a witness, the Prius driver made no attempt to slow down. Four people with a total weight of 460 lb were in the Durango. The only person in the Prius was the 150-lb driver. The Durango with its passengers had a weight of 6500 lb, and the Prius with its driver had a weight of 3042 lb.
Explanation / Answer
Since you have not mentioned anything in the question, I am making an intelligent guess that you/public safety department want to find out the speed of Durango before the collision in order to know whether they broke any law:
Initial momentum of Prius = 3042 lb *50mph = 1379.828*22.352kgm/s
=30842 kgm/s due north
initial momentum of Durango in SI unit = 2948.35 v due east
let the final speed of the system be vf
mass of the system in kg =4328 kg
equating momentum in north direction:
30842 kgm/s = 4328.178 vf sin 39 degree
30842=2724 Vf
vf =11.322 m/s = 25.3 mph..........speed of system after collision
now equating momentum in eastward direction
2948.35 v = 4328.178 vf cos 39 degree
2948.35 v = 4328.178*11.322 *cos 39 degree
v= [4328.178*11.322 *cos 39 degree]/2948.35
v=12.92 m/s = 28.9 mph..............speed of Durango