Answer:
h = 50.6 m
Explanation:
Principle of work and energy
ΔE = W
where:
ΔE: mechanical energy change (J)
W : work of the non-conservative forces (J)
ΔE = Ef-Ei
Ef : final mechanical energy
Ei : initial mechanical energy
K =(1/2 )mv² : Kinetic energy (J)
U= mgh :Potential energy (J)
m: mass (kg)
v : speed (m/s)
h: high (m)
Data
m = 85 kg : mass of the skier
vi = 2 m/s : Initial speed of the skier
vf = 30 m/s : Final speed of the skier
hf = 0 Final high of the skier
W = - 4000 J ; Work of the friction force and force of the air resistance
g = 9.8 m/s² : acceleration due to gravity
Principle of work and energy to the skier
ΔE = Ef-Ei
Ef = Kf + Uf = (1/2 )m(vf)² + mg(hf)= (1/2 )85(30)² + mg(0)= (1/2 )85(30)² J
Ei = Ki + Ui = (1/2 )m(vi)² + mg(hi) = ( (1/2 )85(2)² + 85*9.8(h) ) J
ΔE = Wf
Ef - Ei = Wf
(1/2 )(85)(30)² -( (1/2 )(85)(2)² +( 85)*9.8(h) ) = -4000
We factor 85 and pass it to the other side of the equation to divide
(1/2 )(30)² - (1/2 )(2)² - 9.8 (h) = -4000/85
450 - 1 - 9.8 (h) = -47.0588
449 - 9.8 (h) = -47.0588
449 +47.0588 = 9.8 (h)
496.0588 =9.8 (h)
h =496.0588/ 9.8
h = 50.6 m
