Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 592

Figure 12.10
A bullet fired into a block suspended
by a wire (in other words, a typical
episode of MythBusters )

Now we look for the resulting common velocity, which we'll denote simply as
v ′ , using the law of conservation of momentum, p = p ′ , and the knowledge
that this is an inelastic collision, v ′ = v ′

1 = v ′

2 :

′ ′ ′

p = m 1 v

1 + m 2 v 2 ,

′ ′

3.50 kg m/s = (2.00 kg)v + (10.0 g)v ,

′

3.50 kg m/s = (2.00 kg + 10.0 g)v ,

′

(3.50 kg m/s)/(2.01 kg) = v ,

′

1.74 m/s = v .

Let's look at one more example of an inelastic collision, this time in
2D. Consider a driver who runs a red light and crashes into a car crossing
the intersection. Let's say that Grant is the safe driver, and at the time
of the collision, Grant and his fuel-e cient hybrid have a combined mass
of 1,500 kg and are traveling west at 35 km/hr. Kari, 14 who is not paying
attention, sees Grant's car too late, and swerves to the left. She and her car
have a combined mass of 2,500 kg. At impact, she is traveling at 65 km/hr,
heading 25 o west of north, as shown in Figure 12.11. Assume that we can
treat the collision as inelastic. What is the velocity of the crash just after
the collision? 15
To solve this problem, let's set up a 2D coordinate space where +x is
east and +y is north. We compute the total momentum before the crash

14 We choose to make Kari the bad driver not because of gender bias or because she's
a redhead, but on the assumption that there are fewer Karis than Grants out there to
offend.
15 Another MythBusters moment.