Anonymous

# 2 math questions on 3d car crashes?

Suppose you're coding a car crash in a 3D racing game. A car with a mass of 3000kg has a velocity of (60, -5,-45) when it hits another car of mass 1500kg going (-70,60,-5). If the two cars become entangled in the crash, what's their final velocity?

What about this time the cars don't get stuck together. A car with a mass 1000kg has a velocity (60,-10,-45) when it hits another car of mass 1700kg going (-45,20,-55). Using e=0.5, what should their final velocities be?

Relevance
• Anonymous

1.

Lets call the 3000kg car carA, and the 1500 kg car CarB

carA has of mass of Ma and a velocity vector Va

carB has of mass of Mb and a velocity vector Vb

MaVa + MbVb = (Ma + Mb)Vab

Where Vab is the resultant velocity vector of both cars combined

Vab = (MaVa + MbVb)/(Ma + Mb) = (3000[60 -5 -45] + 1500[-70 60 -5])/(3000 + 1500)

Vab = [75000 75000 -142500]/4500 = [16.666 16.666 -31.666]

2.

MaVa1 +MbVb1 = MaVa2 +MbVb2 (1)

e = (Vb2 - Va2)/(Va1 - Vb1)

e(Va1 - Vb1 ) = Vb2 - Va2 (2)

solve the equations simultaneously

Va2 = (3MaVa1 + (2Ma- Mb)Vb1)/2(Ma + Mb)

Vb2 = (3MbVb1+ (2Mb - Ma)Va1)/2(Ma + Mb)

Va2 = (3(1000)[60 -10 -45] + (2000 - 1700)[-45 20 -55])/2(1000 + 1700) = [30.83 -4.44 -28.06]

Vb2 = (3(1700)[-45 20 -55] +(3400 - 1000)[60 -10 -45])/2(1000 + 1700) = [-15.83 14.44 -71.94]

Using matrices

[[Ma Mb] = A

[-1 1]]

[[Va2] = V

[Vb2]]

[[MaVa1 + MbVb1] = B

[e(Va1 - Vb1]]

AV = B

V = A^-1 B