How high (in m) will the swing be at the high point?

Question

A child on a swing has a speed of 3.7 m/s at the low point of the arc.

How high (in m) will the swing be at the high point?

Answer 1

Take the low point of the swing as 0 height. Conservation of mechanical energy says that kinetic energy at the low point (0 height, max speed) must equal potential energy at the highest point (0 speed, max height).

KE_low = PE_high so 0.5mv² = mgh; divide both sides by m and rearrange: h = 0.5v² / g

= (0.5)(3.7)² / 9.8 = 0.7 m