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A ski lift is used to transport people from the base of a hill to the top. If the lift leaves the base at a velocity of 15.5 m/s and arrives at the top with a final velocity of 0 m/s, what is the height of the hill? Round the answer to the nearest tenth

Respuesta :

Arnold11
This can be calculated with the law of conservation of energy. The sky lift is starting with the speed v= 15.5 m/s and all of it's kinetic energy Ek is transformed to potential energy Ep so the energies have to be equal: Ep=Ek.
Since Ek=(1/2)*m*v² where m is mass and v is the speed, Ep=m*g*h, where m is mass, g= 9.81 m/s² and h is height. Now:

Ek=Ep 

(1/2)*m*v²=m*g*h, masses cancel out,

(1/2)*v²=g*h, divide by g to get the height,

(1/2*g)*v²=h and now plug in the numbers:

h=12.245 m. Height of the hill rounded to the nearest tenth is h=12.25 m 

The height of the hill is 12.25 m. The height of the hill can be calculated from the law of conservation of energy.

How to calculate the height of the hill?

The height of the hill can be calculated from the law of conservation of energy as initial velocity (Kinetic energy) transforms into potential energy (height).

[tex]KE = U[/tex]

Where,

[tex]KE[/tex] = Kinetic energy =[tex]\dfrac 12 mv^2[/tex]

[tex]U[/tex] = potential energy  = [tex]mgh[/tex]

So,

[tex]\dfrac 12 mv^2 = mgh\\\\h = \dfrac 12 \dfrac {mv^2}{g}[/tex]

Where,

[tex]h[/tex] - height = ?

[tex]v[/tex] - velocity = 15.5 m/s

[tex]g[/tex] - gravitational acceleration = 9.8 m/s²

Put the values in the formula,

[tex]h = \dfrac 12 \dfrac {15.5^2}{9.8}\\\\h = 12.25 \rm \ m[/tex]

Therefore, the height of the hill is 12.25 m.

Learn more about potential energy:

https://brainly.com/question/25700533

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