Question

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

Answer 1

Answer:

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

Lemme know if you have any questions :)

Answer 2

It’s C because I took the test and got it right