Question

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

Answer 1

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.