Question

A body of mass 5 kg moving with a speed of $3m{s}^{-1}$ collides head on with a body of mass 3 kg moving in the opposite direction at a speed of $2m{s}^{-1}$. The first body stops after the collision. Find the final velocity of the second body.

• A. $5m{s}^{-1}$
• B. $30m{s}^{-1}$
• C. $-9m{s}^{-1}$
• D. $3m{s}^{-1}$

Answer 1

Answer: (D)

$\underset{–}{Given:}$

$m_1=5kg$

$m_2=3kg$

$u_1=3m{s}^{-1}$

$u_2=-2m{s}^{-1}$

Before collision, the 2nd body is moving backwards. Hence its velocity is negative.

$v_1=0m{s}^{-1}$

After collision, the 1st body stops moving. So its velocity is zero.

$To$ $find:$ $v_2=$ $?$

$\underset{–}{Solution:}$

$m_1{u}_1+m_2{u}_2$ $=$ $m_1{v}_1+m_2{v}_2$

Substituting the values, we get,

$(5\times 3)$ $+$ $(3\times (-2\left)\right)$ $=$ $5\times 0$ $+$ $3\times v_2$

$\therefore 15$ $-$ $6$ $=$ $3\times v_2$

$\therefore$ $9$ $=$ $3v_2$

$\therefore$ $v_2$ $=$ $9$ $÷$ $3$ $=$ $3$

$\therefore$ $v_2$ $=$ $3m{s}^{-1}$

Since we got a positive value for $v_2,$ it means that the 2nd body moves forwards after collision.

Velocity being a vector quantity, the direction is also important.

After collision, the 2nd body moves with a velocity $3m{s}^{-1}$ in the forward direction.