An 80.0 kg student running at 3.5 m/s grabs a rope that is hanging vertically. how high will the student swing?

Ek₀ and ep₀ are initial kinetic and potential energies respectively.ek and ep are final kinetic and potential energies respectively.energy in the system is conserved.ek₀ + ep₀ = ek + epassume student is one some ground ground, so ep₀ = 0at the apex of student's swing, ek = 0ek₀ + 0 = 0+ epek₀ = epmv₀²/2 = mghmass cancels outv₀²/2 = ghh = v₀²/(2g)h = (3.5 m/s)²/(2 * 9.81 m/s²)h = 0.62 mhe will swing 0.62 m high (relative to where he was running before)