Gravitational Potential Energy Lost During the Fall
[tex]\text{Gravitational Potential Energy } = mgh[/tex]
[tex]= (0.06)(10)(1.5)[/tex]
[tex]= 0.9 \text{J}[/tex]
Kinetic Energy Before Impact
As the ball falls, the gravitational energy is converted to kinetic energy. Just before impact, when the ball is just touching the ground, the gravitational potential energy is 0 (as the height above the ground is essentially 0), meaning that all of the gravitational potential energy has been converted. This means that the kinetic energy at this point is 0.9J.
Speed of the Ball Before Impact
[tex]u = 0[/tex]
[tex]a = g = 10 \text{ms}^{-2}[/tex]
[tex]s = 1.5 \text{m}[/tex]
[tex]v^2 = u^2 + 2as[/tex]
[tex]\implies v = \sqrt{u^2 + 2as}[/tex]
[tex]= \sqrt{0^2 + 2(10)(1.5)}[/tex]
[tex]= \sqrt{30} \text{ ms}^{-1}[/tex]
[tex]= 5.5 \text{ms}^{-1}\text{to 2s.f.}[/tex]
Gravitational Potential Energy Gained After Rebound
[tex]\text{Gravitational Potential Energy } = mgh[/tex]
[tex]= (0.06)(10)(1.3)[/tex]
[tex]= 0.78 \text{J}[/tex]
