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When the skater starts 7 above the ground, how does the speed of the skater at the bottom of the track compare to the speed of the skater at the bottom when the skater starts 4 above the ground?
A. twice as fast.
B. higher, but less than twice as fast.
C. the same.
D. four times as fast.

Respuesta :

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Answer:

A. twice as fast.

Explanation:

m = Mass of skater

h = Height from where the skater starts

g = Acceleration due to gravity = 9.81 m/s²

Here the kinetic and potential energies balance each other

[tex]K=P\\\Rightarrow \frac{1}{2}mv^2=mgh\\\Rightarrow v=\sqrt{2gh}[/tex]

Velocity from 7 m

[tex]v_1=\sqrt{2g7}[/tex]

Velocity from 4 m

[tex]v_2=\sqrt{2g4}[/tex]

Dividing the two equations

[tex]\frac{v_1}{v_2}=\frac{\sqrt{2g7}}{\sqrt{2g4}}\\\Rightarrow \frac{v_1}{v_2}=1.32\approx 2\\\Rightarrow v_1\approx 2v_2[/tex]

So, the velocity of the skater is twice as fast

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