A 1200 kg car is moving at 5.0 m/s EAST. It strikes an 1800 kg car at rest. The cars undergo an elastic collision and move in the EAST or WEST direction. The velocity of the 1800 kg car after the collision is
A) 3.0 m/s WEST.
B) 1.0 m/s EAST.
C) 4.0 m/s EAST.
D) 4.0 m/s WEST.
E) 1.0 m/s WEST.

Question

Quizplus · Accepted Answer

We can use conservation of momentum to solve for the final velocity of the 1800 kg car. 
Initial momentum: 
p = m1v1 + m2v2 = (1200 kg)(5.0 m/s) + (1800 kg)(0 m/s) = 6000 kg m/s to the EAST
Final momentum: 
p' = m1v1' + m2v2' 
Since the collision is elastic, kinetic energy is conserved as well as momentum, so we can use the following equations: 
m1v1 + m2v2 = m1v1' + m2v2' 
(1/2)m1v1^2 + (1/2)m2v2^2 = (1/2)m1v1'^2 + (1/2)m2v2'^2 
Solving for v2': 
v2' = [m1v1 + m2v2 - m1v1']/m2 
Substituting in the values: 
v2' = [(1200 kg)(5.0 m/s) + (1800 kg)(0 m/s) - (1200 kg)v1']/1800 kg 
v2' = 5/3 - (4/3)v1' 
We also know that the total momentum after the collision needs to equal 6000 kg m/s to the EAST, so: 
m1v1' + m2v2' = 6000 kg m/s 
(1200 kg)v1' + (1800 kg)v2' = 6000 kg m/s 
Substituting in the expression for v2' from the previous equation: 
(1200 kg)v1' + (1800 kg)(5/3 - (4/3)v1') = 6000 kg m/s 
Simplifying: 
800 kg v1' = 2000 kg m/s 
v1' = 2.5 m/s EAST 
Substituting back into the expression for v2': 
v2' = 5/3 - (4/3)(2.5 m/s) 
v2' = 4.0 m/s EAST 
Therefore, the correct answer is C, 4.0 m/s EAST.

A 1200 Kg Car Is Moving at 5