You are an investigator at the scene of a car crash. A Volvo of has hit an Alpha
ID: 1789828 • Letter: Y
Question
You are an investigator at the scene of a car crash. A Volvo of has hit an Alpha Romeo from the side and the two are inter-tangled (stuck together). You can see that the Volvo was traveling due east on a road with a 50 mph speed limit and made a 30.0 m long skid mark before reaching the intersection where it hit the Alpha Romeo which was driving due North on a road with a 25 mph speed limit. There are additional skid marks from both cars that are 12.25 m long at 15 degrees North of East. Further investigation tells you that the mass of the Volvo (including the driver) is 1650 kg and the mass of the Alpha Romeo (including the driver) is 975 kg. You recognize that the accident occurred on dry concrete roads, each of which had a 45 mph speed limit. Your task is to determine if either car was speeding. 1. Determine the speed of the Volvo before it slammed on the brakes. 2. Find the speed of the Alpha Romeo when it was hit by the Volvo.Explanation / Answer
speed of volvo, ui ( i is unit vector in east direction, j is unit vectro in north direction)
skid marks of volvo before colliding, d = 30 m
speed limit = 50 mph
Mass, M = 1650 kg
alpha romeo, speed = Uj, speed limit = 25 mph
mass, m = 975 kg
final skid mark length = l = 12.25 m in theta = 15 degreres north of east
so lets say after collsiioon the speed of b oth cars is v
now, kinetic coefficient of friciton between rubber and concrete is about k = 0.8
so, k(M + m)g*l = 0.5(M + m)v^2 [ work done against freiciton = kinetic energy of both cars after collision]
v = sqroot(2k*gl) = 13.866 m/s
a.
from conservation of momentum
Mu = (M + m)vcos(15)
1650*u = (1650 + 975)*13.866cos(15)
u = 21.308 m/s
speed of volvo before it slammed brakes = u'
then from conservation of energy
0.5Mu'^2 = kMgd + 0.5Mu^2
u'^2 = u^2 + 1.6*9.81*30
u' = 30.412 m/s = 68.0297065 mph
so volvo was overspeeding
b. from conservation of momentum
m*U = (m + M)vsin(15)
U = 9.6621 m/s ( weasnt overspeeding)
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