Question

A heavy car $A$ of mass $2000kg$ travelling at $10m/s$ has a head-on collision with a sports car$B$ of mass $500kg$. If both cars stop dead on colliding, what was the velocity of car $B$?

Answer 1

Step 1. Given data

Mass of Car $A$, $=2000kg$

Speed of Car $A$, $=10m/s$

Mass of Car $B$, $=500kg$

We need to find speed of Car $B$, $v_B$

Step 2. Formula used

The linear momentum $P$ of an object is given by

$P=mv$

where $m$ is the mass of the object and $v$the velocity of the object

Step 3. Find the velocity of the car $B$

$$\begin{gathered} m_A=2000kg \\ {m}_B=500kg \\ {v}_A=10m/s \end{gathered}$$

We have to find the velocity of the car $B$ before the collision.

After the collision, both cars stop. So after the collision, the velocity of the cars is zero.

According to the law of conservation of linear momentum, the sum of linear momentum of the car $A$ and $B$ before the collision is equal to the sum of linear momentum of the car $A$ and $B$after the collision.

$$\begin{gathered} \therefore m_A{v}_A+m_B{v}_B=0 \\ \Rightarrow v_B=-\frac{m_A{v}_A}{m_B} \\ \Rightarrow v_B=-\frac{2000\times 10}{500} \\ \Rightarrow v_B=-40m/s \end{gathered}$$

Hence, the velocity of the car $B$ is $40m/s$.