An 800 kg car moving at 4 m/sec to the right strikes a 400 kg car moving to the left. If the cars stick together and stop moving right after the collision, what was the velocity of the 400 kg car?
A) It was stationary
B) 2 m/sec to the left
C) 8 m/sec to the left
D) 4 m/sec to the left

Question

Quizplus · Accepted Answer

To solve this, we use the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision. The formula for momentum is $p = mv$, where $m$ is mass and $v$ is velocity. Before the collision, the momentum of the 800 kg car is $800 \times 4 = 3200 \, \text{kg m/s}$ to the right, and let's denote the velocity of the 400 kg car as $v$. The total momentum before the collision is $3200 + 400v$ (noting that $v$ will be negative since it's to the left). After the collision, the cars stick together and stop, so their total momentum is 0. Setting the total momentums equal gives $3200 + 400v = 0$, solving for $v$ gives $v = -8 \, \text{m/sec}$, which means the 400 kg car was moving at 8 m/sec to the left.

An 800 Kg Car Moving at 4 M/sec to the Right