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 concrete 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 concrete 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. 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.

Answer 1

given, speed of V beofre collision, Uv east, 50 mph speed limit
speed of V just before collision = uv
length of skid marks of V, dv = 30 m

given, speed of R beofre collision, Ur = north, 25 mph speed limit
speed of R just before collision = ur
Ur = ur

combined skid mark length, l = 12.25 m
theta = 15 deg north of east
Mv = 1650 kg
Mr = 975 kg

now,
from conservation of momentum

Mv*uv = (Mv + Mr)v*cos(theta)
Mr*ur = (Mv + Mr)v*sin(theta)
also

v^2 = 2*a*l

hence
tan(theta) = ur/uv = 0.2679491

for dry road coefficient of friciton = 0.6
then
a = 0.6g
hence
v = 12.008621902616 m/s

hence
uv = 18.4536514175 m/s
ur = 4.944640994733 m/s

now,
Uv^2 - uv^2 = 2*0.6*g*dv
Uv = 26.3381330135 m/s = 58.91672560 mph
and Ur = ur = 11.060846892298228 mph

hence, Uv > speed limit, Ur < speed limit