Work, Energy and Power — Question 4

As the person swings on a rope from a cliff of height h = 20 m then potential energy at the top gets converted into kinetic energy at the lowest point.

From conservation of energy,

Potential energy at top = Kinetic energy at lowest point

mgh = $\dfrac{1}{2}$mv²

gh = $\dfrac{1}{2}$v²

10 x 20 = $\dfrac{1}{2}$v²

400 = v²

$v=\sqrt{400}=20$ m/s

∴ The person is moving at a speed of 20 m/s at the lowest point of the swing.