Answer :
Explanation:
As per the law of conservation of energy, the final mechanical energy of Lora is equal to its initial mechanical energy. So, when Lora is at the bottom of ski run then her potential energy will change into kinetic energy.
Hence, [tex]E_{initial} = \frac{mv_{i}^{2}}{2} + mgh [/tex]
[tex]E_{final} = \frac{mv_{f}^{2}}{2}[/tex]
Now, final kinetic energy that will be at the bottom of the ski run is as follows.
Let, [tex]E_{k} = E_{final}[/tex]
[tex]E_{intial} = E_{final}[/tex]
[tex]E_{k} = \frac{mv_{i}^{2}}{2} + mgh [/tex]
= [tex]\frac{(43.6 \times (3.6)^{2}}{2} + (43.6 \times 9.81 \times 67)[/tex]
= 282.53 + 28656.97
= 28939.502 J
Thus, we can conclude that her final kinetic energy at the bottom of the ski run is 28939.502 J.
The final kinetic energy will be equal to the kinetic energy and potential energy. The final kinetic energy of Lora will be 28936.5 J.
The final kinetic energy:
[tex]K_f = \dfrac 12 mv^2 +mgh[/tex]
Where,
[tex]m[/tex] - mass = 43.6 kg
[tex]v[/tex] - velocity = 3.6 m/s
[tex]g[/tex] - gravitational acceleration
[tex]h[/tex] - height = 67 m
Put the values in the formula,
[tex]K_f = \dfrac 12 43.6 \times 3.6 ^2 +43.6 \times 9.8 \times 67\\\\K_f = 28939.502 \rm \ J.[/tex]
Therefore, the final kinetic energy of Lora will be 28936.5 J.
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