Question

Three blocks are initially placed as shown in the figure. Block $A$ has mass $m$ and initial velocity $v$ to the right. Block $B$ with mass $m$ and block $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block $A$ is

• A. $0.60v$ to the left
• B. $1.4v$ to the left
• C. $v$ to the left
• D. $0.4v$ to the left

Answer 1

The correct option is A $0.60v$ to the left

After first Collision, velocities are interchanged between A and B,

Second Collision

$mv+4m\left[0\right]=-m{v}_1+4m{v}_2\dots \dots \left(1\right)$
$e=-\left[\frac{v_2-[-v_1]}{0-\left[v\right]}\right]$
for elastic collision $e=1$
$1=-\left[\frac{v_1+v_1}{-v}\right]$
$v_2+v_1=v$
$v_2=v-v_1$
put $v_2$ value in equation (1):
$mv=-m{v}_1+4m[v-v_1]$
$mv=-mv+4mv-4m{v}_1$
$5m{v}_1=3mv$
$v_1=\frac{3v}{5}=0.60v$ to the left
Third collision:

After collision the velocity of block ${}^{\prime }{A}^{\prime }$ inter-exchange with block ${}^{\prime }{B}^{\prime }$.