A 1200-kg car moving at $15.6 \mathrm {~m} / \mathrm { s }$ suddenly collides with a stationary car of mass $1500 \mathrm {~kg} \text {. }$ If the two vehicles lock together,what is their combined velocity immediately after the collision?
A)6.9 m/s
B)8.6 m/s
C)12.1 m/s
D)5.5 m/s

Question

Quizplus · Accepted Answer

The conservation of momentum principle states that the total momentum before the collision is equal to the total momentum after the collision. Before the collision, the total momentum is $1200 \, \text{kg} \times 15.6 \, \text{m/s}$ (since the second car is stationary, it contributes no initial momentum). After the collision, the combined mass is $1200 \, \text{kg} + 1500 \, \text{kg} = 2700 \, \text{kg}$, and they move together with a velocity $v$. Setting the initial momentum equal to the final momentum, $1200 \times 15.6 = 2700 \times v$, solving for $v$ gives $v = 6.9 \, \text{m/s}$.

A 1200-Kg Car Moving At 15.6 m/s15.6 \mathrm {~m} / \mathrm { s }15.6 m/s

A 1200-Kg Car Moving At $15.6 \mathrm {~m} / \mathrm { s }$