Conservation of Momentum in Inelastic Collision

Steps:

• Calculate x-momentum before: $0.2 \times 0.5 = 0.1$ kg m/s.
• Calculate y-momentum before: $0.3 \times 0.4 = 0.12$ kg m/s.
• Total mass after collision: $0.2 + 0.3 = 0.5$ kg.
• $\tan \theta = \frac{0.12}{0.1} = 1.2$, so $\theta = \tan^{-1}(1.2) \approx 50^\circ$.

Why C is correct:

• Momentum conservation gives $\tan \theta =$ (y-momentum)/(x-momentum) = 1.2, and $\tan^{-1}(1.2) = 50^\circ$.

Why the others are wrong:

• A: $37^\circ$ matches $\tan^{-1}(0.75)$, wrong ratio.
• B: $40^\circ$ matches , wrong ratio.

Final answer: C