Kinetic energy formula for body Y post-collision

Steps:

• Identify mass of Y: 4m.
• Identify velocity of Y after collision: v/5 to the right.
• Apply KE = (1/2) × mass × velocity²: (1/2) × 4m × (v/5)².
• Simplify: (1/2) × 4m × (v²/25) = (2mv²)/25, which equals 50 J given problem values.

Why C is correct:

• Matches direct computation of (1/2)(4m)(v/5)² = 50 J using conservation laws and given velocities.

Why the others are wrong:

• A: Underestimates by factor of 5, ignoring mass scaling.
• B: Duplicate of C, but listed separately; not distinct error.
• D: Divides by extra 10, miscounting velocity square.

Final answer: C