Question

Astronauts Mr X (mass 120 kg) and Mr Y( mass 90 kg) float in negative free space with no relative velocity to one another. Mr Y throws a mass of 5 kg towards Mr X moving with speed of 2 ms${}^{-1}$. If Mr X catches it, the change in velocity of X and Y are :

• A. 0.21 and 0.80 ms${}^{-1}$
• B. 0.80 and 0.21 ms${}^{-1}$
• C. 0.12 and 0.08 ms${}^{-1}$
• D. 0.08 and 0.12 ms${}^{-1}$

Answer 1

Answer: (D)

0.08 and 0.12 ms${}^{-1}$

Let the final velocities of X and Y be $V_X$ and $V_Y$, respectively.

Using conservation of linear momentum for "X + mass thrown" system : $P_{initial}=P_{final}$

$\therefore$ $0=M_b{V}_b-M_x{V}_X$

Or $0=\left(5\right)\left(2\right)-\left(120\right)V_X$

$⟹$ $V_X=0.08m/s$

For Y+ mass thrown system :

Initial velocity of astronaut Y is zero. After it catches the mass, both the mass and the astronaut Y move with common velocity $V_Y$.

Using conservation of linear momentum for "Y + mass thrown" system : $P_{initial}=P_{final}$

$\therefore$ $M_b{V}_b+0=(M_Y+M_b)V_Y$

Or $\left(5\right)\left(2\right)+0=(90+5)V_Y$

$⟹$ $V_Y=\frac{10}{95}=0.12m/s$