Kinetic energy scales with the square of velocity

Steps:

• Kinetic energy formula: KE = (1/2) m v² for any object.
• For X: KE_X = (1/2) m v².
• For Y: KE_Y = (1/2) m (2v)² = (1/2) m (4v²) = 4 × [(1/2) m v²] = 4 KE_X.
• Ratio KE_Y / KE_X = 4.

Why C is correct:

• The ratio follows directly from the KE formula, as masses are equal and velocity doubles, squaring to 4.

Why the others are wrong:

• A (1): Ignores velocity difference; ratio would be 1 only if velocities matched.
• B (2): Assumes linear scaling with velocity, but KE is quadratic.
• D (8): Overcounts; doubling velocity quadruples KE, not octuples.

Final answer: C