A person stands at rest on a slope which makes an angle 25 degrees to the horizontal. They have a mass of 71 kg. They start to run up the slope. After a time of 9.9 s they reach a distance 29 m up the slope and have a velocity of 4.7 m/s.
(a) Calculate the vertical height gained.
select units
(b) Determine how much energy the person has used.
select units
(c) Calculate the average power output of the person.
select units

a) 12.2559 m

b) 9320.5519 J

c) 941.4699 W

Explanation:

a) Use sine to find vertical height.

sinθ = opposite/hypotenuse

∴ sin25 = h/29

∴ h = 29 (sin25) = 12.25592959 metres

b) Find mechanical energy using potential and kinetic energy.

Total energy used is mechanical energy. Menchanical energy (E) is equal to potential energy (U=mgh) plus kinetic energy (K= (0.5)m v²).

E = U + K

= mgh + (0.5)m v²

= (71)(9.81)(12.2559) + (0.5)(71)(4.7²)

= 8536.356909 + 784.195

= 9320.551909 Joules

c) Find power using answer from part b

Power = energy / time elapsed

= 9320.5519/9.9

= 941.4698898 Watts

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