Roller coaster and speed-have answer need help getting there.

Question

A roller coaster starts from rest at its highest point and then descends on its (frictionless) track. Its speed is 34 m/s when it reaches ground level. What was its speed when its height was half that of its starting point?

Answer: 24 m/s

Answer 1

mgh = mv²/2; h = v²/2g; mgv²/4g + mv_x²/2 = mv²/2; v_x² = v²/2; v_x = v/√2 = 244 m/s