Conservation of Mechanical Energy

Steps:

• Initial total energy is kinetic energy (KE_i = ½mv²), potential energy (PE) = 0.
• At maximum height H = v²/(2g), PE = mgH = KE_i, KE = 0; total energy conserved.
• Midpoint height = H/2, so PE = mg(H/2) = ½ KE_i; KE = ½ KE_i.
• Compare statements to energy conservation principle.

Why B is correct:

• At midpoint, PE = ½ initial KE (from PE = mgh with h = H/2 and mgH = initial KE), not equal to initial KE.

Why the others are wrong:

• A: Correct, as work against gravity converts KE to PE during ascent.
• C: Correct, velocity is zero at peak, so KE = 0.
• D: Incorrect statement; total energy equals initial total energy, not less (no dissipation assumed).

Final answer: B