Answer:
a) [tex]U_{g} = 40\,J[/tex], b) [tex]\eta = 70\,\%[/tex], c) [tex]v = 20\,\frac{m}{s}[/tex]
Explanation:
a) The initial potential energy is:
[tex]U_{g} = (0.2\,kg)\cdot \left(10\,\frac{m}{s^{2}} \right)\cdot (20\,m)[/tex]
[tex]U_{g} = 40\,J[/tex]
b) The efficiency of the bounce is:
[tex]\eta = \left(\frac{14\,m}{20\,m} \right)\times 100\,\%[/tex]
[tex]\eta = 70\,\%[/tex]
c) The final speed of Danielle right before reaching the bottom of the hill is determined from the Principle of Energy Conservation:
[tex]K = U_{g}[/tex]
[tex]U_{g} = \frac{1}{2}\cdot m \cdot v^{2}[/tex]
[tex]v = \sqrt{\frac{2\cdot U_{g}}{m} }[/tex]
[tex]v = \sqrt{\frac{2\cdot (40\,J)}{0.2\,kg} }[/tex]
[tex]v = 20\,\frac{m}{s}[/tex]
