Question

Two skaters A and B of mass $M$ and $2M$ are standing together on a frictionless ice surface. They push each other apart. The skater $B$ moves away from $A$ with a speed of $8m/s$ relative to ice. The separation between the two skaters after $5$ seconds will be

• A. $30m$
• B. $32m$
• C. $40m$
• D. none of these

Answer 1

The correct option is D none of these

Given,

$v_B=8m/s$

$M_A=M$

$M_B=2M$

When B pushes A to gain $8m/s$ velocity,

As there are no external forces acting on $AB$ system,

Momentum of $AB$ must be conserved.

$p_i=p_f$

$0=2M\times 8-M\times V_A$ (as A will move pposite to B)

$V_A=16m/s$

Now total separation between $AandB$ after $5sec$

$=8\times 5+16\times 5=120m$

Hence option $\text{D}$ is correct answer.