If a 140 lb. climber saved her potential energy as she descended from Mt. Everest (Elev. 29,029 ft) to Kathmandu (Elev. 4,600 ft), how long

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If a 140 lb. climber saved her potential energy as she descended from Mt. Everest (Elev. 29,029 ft) to Kathmandu (Elev. 4,600 ft), how long could she power her 0.4 watt flashlight

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RobertKer 4 years 2021-08-12T19:52:05+00:00 1 Answers 15 views 0

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  1. quangkhai
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    2021-08-12T19:53:23+00:00
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    Answer: 3217.79 hours.

    Explanation:

    Given, A 140 lb. climber saved her potential energy as she descended from Mt. Everest (Elev. 29,029 ft) to Kathmandu (Elev. 4,600 ft).

    Power = 0.4 watt

    Mass of climber = 140 lb

    = 140 x 0.4535 kg  [∵ 1 lb= 0.4535 kg]

    ⇒ Mass of climber (m) = 63.50 kg

    Let h_1=29,029\ ft= 8848.04\ m\ \ \ \ [ 1 ft=0.3048\ m ] and h_2= 4,600 ft = 1402.08\ m

    Now, Energy saved =mg(h_1-h_2)=(63.50)(9.8)(8848.04-1402.08)=4633620.91\ J

    \text{Power}=\dfrac{\text{energy}}{\text{time}}\\\\\Rightarrow 0.4=\dfrac{4633620.91}{\text{time}}\\\\\Rightarrow\ \text{time}=\dfrac{4633620.91}{0.4}\approx11584052.28\text{ seconds}\\\\=\dfrac{11584052.28}{3600}\text{ hours}\ \ \ [\text{1 hour = 3600 seconds}]\\\\=3217.79\text{ hours}

    Hence, she can power her 0.4 watt flashlight for 3217.79 hours.

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