Answer: 17.14 m/s
Explanation:
We can solve this problem applying the Conservation of Mechanical energy (which is the sum of the kinetic energy [tex]K[/tex] and potential energy [tex]P[/tex]), where the total initial mechanical energy [tex]E_{o}[/tex] must be equal to the total final mechanical energy [tex]E_{f}[/tex]:
[tex]E_{o}=E_{f}[/tex] (1)
Being:
[tex]E_{o}=K_{o}+P_{o}=\frac{1}{2}mV_{o}^{2}+mgh_{o}[/tex] (2)
[tex]E_{f}=K_{f}+P_{f}=\frac{1}{2}mV_{f}^{2}+mgh_{f}[/tex] (3)
Where:
[tex]m=8.1 kg[/tex] is the mass of the object
[tex]V_{o}=0 m/s[/tex] is the initial velocity (the object was at rest)
[tex]g=9.8 m/s^{2}[/tex] is the acceleration due gravity
[tex]h_{o}=15 m[/tex] is the object's initial height or position
[tex]V_{f}[/tex] is the final velocity
[tex]h_{f}=0 m[/tex] is the object's final height or position
Solving and applying the given conditions:
[tex]\frac{1}{2}mV_{o}^{2}+mgh_{o}=\frac{1}{2}mV_{f}^{2}+mgh_{f}[/tex] (4)
[tex]mgh_{o}=\frac{1}{2}mV_{f}^{2}[/tex] (5)
Finding [tex]V_{f}[/tex]:
[tex]V_{f}=\sqrt{2gh_{o}}[/tex] (6)
[tex]V_{f}=\sqrt{2(9.8 m/s^{2})(15 m)}[/tex] (7)
Finally:
[tex]V_{f}=17.14 m/s[/tex]
