Work, Energy and Power — Question 7

Given,

Energy lost = 0.6 x KE

KE = $\dfrac{1}{2}$ x mass x velocity²

Substituting the values we get,

$KE = \dfrac{1}{2} \times mass \times 5^2 \\[0.5em]$

Amount of energy lost,

$\text{Energy lost} = \dfrac{1}{2} \times mass \times 5^2 \times 0.6 \\[0.5em]$

Amount of energy available,

$\text{Energy available} = \dfrac{1}{2} \times mass \times 5^2 \times 0.4\\[0.5em]$

Applying the rule for the conservation of energy we get,

Kinetic energy available = potential energy

$\dfrac{1}{2} \times mass \times 5^2 \times 0.4 = mass \times gravity \times height\\[0.5em] \Rightarrow \dfrac{1}{2} \times 5 \times 5 \times 0.4 = 10 \times height\\[0.5em] \Rightarrow \dfrac{1}{2} \times 5 \times 2 = 10 \times height\\[0.5em] \Rightarrow 5 = 10 \times height\\[0.5em] \Rightarrow height = 0.5m \\[0.5em]$

∴ Maximum vertical height reached = 0.5m