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What average mechanical power (in W) must a 64.5 kg mountain climber generate to climb to the summit of a hill of height 285 m in 49.0 min? Note: Due to inefficiencies in converting chemical energy to mechanical energy, the amount calculated here is only a fraction of the power that must be produced by the climber's body.

Respuesta :

Answer:61.275 W

Explanation:

Given

Mass of climber [tex]m=64.5 kg[/tex]

Height to climb [tex]h=285 m[/tex]

Time taken [tex]t=49 min \approx 2940 s[/tex]

Now Using  Work-energy Theorem work done is given by

[tex]W=m g h[/tex]

[tex]W=64.5\times 9.8 \times 285[/tex]

[tex]W=180148.5 J[/tex]

[tex]W=180.148 kJ[/tex]

Now  Average Mechanical Power is given by

[tex]P=\frac{W}{\Delta t}[/tex]

[tex]P=\frac{180.148}{2940}=0.0612 kW[/tex]

[tex]P=61.275 W[/tex]