2-D Inelastic Collision Examples
Example 1
A 1500 kg car traveling North at 69 km collides at an intersection with a 3000. kg truck
h
traveling East at 55 km as shown below. If the car and truck stick together during
h
the collision, what is the velocity of the car truck system after the collision?
2-D Inelastic Collision Examples
Example 1
A 1500 kg car traveling North at 69 km collides at an intersection with a 3000. kg truck
h
traveling East at 55 km as shown below. If the car and truck stick together during
h
the collision, what is the velocity of the car truck system after the collision?

pTi

pf


pCi
 
Pi  Pf



pTi  pCi  Pf

pf


pTi

pCi
2-D Inelastic Collision Examples
Example 1
A 1500 kg car traveling North at 69 km collides at an intersection with a 3000. kg truck
h
traveling East at 55 km as shown below. If the car and truck stick together during
h
the collision, what is the velocity of the car truck system after the collision?
 
Pi  Pf



pTi  pCi  Pf

pf

2
p 2f  pTi2  pCi
mT  mc v f 

pCi

pTi
vf 
2
 mT vTi   mC vCi 
2
mT vTi   mC vCi 
2
vf 


3000. kg 55 km
2
2
mT  mC



h
2

 1500 kg 69 km
3000. kg  1500 kg


h
2
2-D Inelastic Collision Examples
Example 1
A 1500 kg car traveling North at 69 km collides at an intersection with a 3000. kg truck
h
traveling East at 55 km as shown below. If the car and truck stick together during
h
the collision, what is the velocity of the car truck system after the collision?
 
Pi  Pf



pTi  pCi  Pf

pf


pTi
v f  43 km
h
1 

pCi
pCi 
  tan 

 pTi 
vCi 
  tan 



m
v
 T Ti 
1  mC


 

 1500 kg 69 km
h
  tan 1 
3000. kg 55 km h
2-D Inelastic Collision Examples
Example 1
A 1500 kg car traveling North at 69 km collides at an intersection with a 3000. kg truck
h
traveling East at 55 km as shown below. If the car and truck stick together during
h
the collision, what is the velocity of the car truck system after the collision?
 
Pi  Pf



pTi  pCi  Pf

pf


pTi
v f  43 km
h
  32

pCi

v f  43 km at 32 N of E
h
2-D Inelastic Collision Examples
Example 2
The Ballistic Pendulum - A 10. g bullet is fired at a 6.0 kg ballistic pendulum. The bullet
becomes embedded in the pendulum and raises it 5.0 cm.
What was the initial velocity of the bullet?

vbi
m
M
h
2-D Inelastic Collision Examples
Example 2
The Ballistic Pendulum - A 10. g bullet is fired at a 6.0 kg ballistic pendulum. The bullet
becomes embedded in the pendulum and raises it 5.0 cm.
What was the initial velocity of the bullet?
Conservation of Momentum
i = just before collision
Conservation of Energy
f = just after collision
f = at maximum height
 
pi  p f


mvbi  ( M  m)v f

vf 
m 
vbi
M m
i = just after collision
0  Eint
0  Ek  Eg
0  Ekf  Eki  Egf  Egi
Eki  Egf
1
( M  m)vi2  M  m gh
2
vi  2 gh
2-D Inelastic Collision Examples
Example 2
The Ballistic Pendulum - A 10. g bullet is fired at a 6.0 kg ballistic pendulum. The bullet
becomes embedded in the pendulum and raises it 5.0 cm.
What was the initial velocity of the bullet?
m
vbi  2 gh
M m
M  m

vbi  
 2 gh
 m 
Ballistic
Pendulum
 6.0 kg  0.010 kg   N 
vbi  
 2 9.8 kg 0.050 m 

0.010 kg

 
vbi  6.0 102 m
s