Question

Two ice skaters $A$ and $B$ approach each other at right angles. Skater $A$ has a mass $30\, kg$ and velocity $1 \,m / s$ and skater $B$ has a mass $20\, kg$ and velocity $2\, m / s$. They meet and cling together. The final velocity of the couple is

• A. 2 m / s
• B. 1.5 m / s
• C. 1 m / s
• D. 2.5 m / s

Answer 1

Answer: (C)

Applying principle of conservation of linear momentum,
$ p=\sqrt{p_{1}^{2}+p_{2}^{2}} $
or $\left(m_{1}+m_{2}\right) v=\sqrt{\left(m_{1} v_{1}\right)^{2}+\left(m_{2} v_{2}\right)^{2}} $
or $ (30+20) v=\sqrt{(30 \times 1)^{2}+(20 \times 2)^{2}}=50 $
$\therefore v=\frac{50}{50}=1\, m / s $