Question

A car A of mass $1500\text{kg}$ is travelling at $25{\text{m s}}^{-1}$ collides with another car B of mass $1000\text{kg}$ travelling at $15{\text{m s}}^{-1}$ in the same direction. After collision, the velocity of car A reduces to $20{\text{m s}}^{-1}$. Calculate the velocity of car B after the collision.

• A. $32.5{\text{m s}}^{-1}$
• B. $35.0{\text{m s}}^{-1}$
• C. $22.5{\text{m s}}^{-1}$
• D. $25.0{\text{m s}}^{-1}$

Answer 1

The correct option is C $22.5{\text{m s}}^{-1}$

Given, mass of car A, $m_1=1500\text{kg}$; initial velocity of car A, $u_1=25{\text{m s}}^{-1}$; initial velocity of car B, $u_2=15{\text{m s}}^{-1}$; mass of car B, $m_2=1000\text{kg}$ and final velocity of car A, $v_1=20{\text{m s}}^{-1}$.
Let final velocity of car B be $v_2$.
According to law of conservation of momentum, we know
$m_1\times u_1+m_2\times u_2$ $=m_1\times v_1+m_2\times v_2$
Substituting in the equation, we get,
$1500\times 25+1000\times 15$ $=1500\times 20+1000v_2$
$\Rightarrow 52500=30000+1000v_2$
$\Rightarrow 22500=1000v_2$
$\Rightarrow v_2=22.5{\text{m s}}^{-1}$